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· negative roots of the characteristic equation



 

1. Node

· negative roots of the characteristic equation

o roots of different signs

o zero roots

o complex roots

o imaginary roots

 

2. node

· positive roots of the characteristic equation

o roots of different signs

o zero roots

o complex roots

o imaginary roots

3. stable node

· negative roots of the characteristic equation

o roots of different signs

o zero roots

o complex roots

o imaginary roots

4. unstable node

· positive roots of the characteristic equation

o roots of different signs

o zero roots

o complex roots

o imaginary roots

 

5. node

· negative or positive roots of the characteristic equation

o roots of different signs

o zero roots

o complex roots

o imaginary roots

6. focus

· The real part of the roots of the characteristic equation is negative

o Roots of different signs

o Zero roots

o Complex roots

o Imaginary roots

7. Focus

· The real part of the roots of the characteristic equation is positive

o Roots of different signs

o Zero roots

o Complex roots

o Imaginary roots

8. Stable focus

· The real part of the roots of the characteristic equation is negative

o Roots of different signs

o Zero roots

o Complex roots

o Imaginary roots

9. Unstable focus

· The real part of the roots of the characteristic equation is positive

o Roots of different signs

o Zero roots

o Complex roots

o Imaginary roots

10. Focus

· The real part of the roots of the characteristic equation is negative and positive

o Roots of different signs

o Zero roots

o Complex roots

o Imaginary roots

11. Center

· The real part of the roots of the characteristic equation is zero

o Roots of different signs

o Zero roots

o Complex roots

o Imaginary roots

 

 

12. Center

· imaginary roots of the characteristic equation

o Roots of different signs

o Zero roots

o Complex roots

o Multiple roots

 

13. Saddle

· The real roots of the different signs of the characteristic equation

o multiple roots

o Zero roots

o Complex roots

o Imaginary roots

 

14. Saddle

· imaginary roots are zero, the real roots of different signs of the characteristic equation

o multiple roots

o Zero roots

o Complex roots

o Imaginary roots

 

15. Node

· negative eigenvalues of the linear part

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

 

16. node

· positive eigenvalues ​​of the linear part

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

 

17. stable node

· negative eigenvalues ​​of the linear part

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

18. unstable node

· positive eigenvalues ​​of the linear part

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

19. node

· positive or negative eigenvalues of the linear part

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

20. focus

· the real part of the eigenvalues of the linear part is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

21. focus

· the real part of the eigenvalues ​​of the linear part is positive

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

22. stable focus

· the real part of the eigenvalues ​​of the linear part is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

23. unstable focus

· the real part of the eigenvalues ​​of the linear part is positive

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues



o imaginary eigenvalue

24. focus

· the real part of the eigenvalues of the linear part of the negative or positive

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

 

25. center

· the real part of the eigenvalues ​​of the linear part is zero

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

26. center

· imaginary eigenvalues

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o multiple eigenvalues

27. saddle

· real eigenvalues ​​of different signs

o multiple eigenvalues

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

28. saddle

· imaginary eigenvalues ​​are equal to zero, the real eigenvalues ​​of different signs

o multiple eigenvalues

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

29. node

· negative eigenvalues ​​of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

30. node

· positive eigenvalues ​​of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

31. stable node

· negative eigenvalues ​​of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

32. unstable node

· positive eigenvalues of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

33. node

· negative or positive eigenvalues ​​of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

34. focus

· the real part of the eigenvalues of the Jacobi matrix is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalue

35. focus

· the real part of the eigenvalues ​​of the Jacobi matrix is positive

o the eigenvalues ​​of different signs

o zero eigenvalues

o multiple eigenvalues

o imaginary eigenvalue

36. stable focus

· the real part of the eigenvalues ​​of the Jacobi matrix is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o multiple eigenvalues

o imaginary eigenvalue

37. unstable focus

· the real part of the eigenvalues ​​of the Jacobi matrix is positive

o the eigenvalues ​​of different signs

o zero eigenvalues

o multiple eigenvalues

o imaginary eigenvalue

38. focus

· the real part of the eigenvalues ​​of the Jacobi matrix is negative or positive

o the eigenvalues ​​of different signs

o zero eigenvalues

o multiple eigenvalues

o imaginary eigenvalue

39. center

· the real part of the eigenvalues ​​of the Jacobi matrix is zero

o the eigenvalues ​​of different signs

o zero eigenvalues

o complex eigenvalues

o multiple eigenvalues

40. center

· imaginary eigenvalues ​​of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o complex eigenvalues

o multiple eigenvalues

41. saddle

· real eigenvalues ​​of the Jacobi matrix of different signs

o multiple eigenvalues

o zero eigenvalues

o complex eigenvalues

o imaginary eigenvalues

42. saddle

· imaginary eigenvalues ​​of the Jacobi matrix are equal to zero, the real eigenvalues ​​of the Jacobi matrix

o multiple eigenvalues

o zero eigenvalues

o complex eigenvalues

o imaginary eigenvalues

43. The fixed point

· the equilibrium position

o an isolated point

o bifurcation point

o the center of the circle

o the center point of gravity

44. The equilibrium position

· fixed point

o an isolated point

o bifurcation point

o the center of the circle

o the center point of gravity

45. The stationary solution

· fixed point

o an isolated point

o bifurcation point

o the center of the circle

o the center point of gravity

46. The equilibrium position

· steady-state solution

o an isolated point

o bifurcation point

o the center of the circle

o the center point of gravity

47. bounded solution

· Lyapunov stable

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

48. Asymptotically stable solution

· Tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

49. Asymptotically stable solution

· bounded solution and tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

50. Asymptotically stable in the whole solution

· tends to zero for the end of the initial conditions

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

51. Asymptotically stable solution

· Tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

52. Asymptotically stable in the whole solution

· Tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

53. Asymptotically stable in the whole solution

· tends to zero for any initial conditions

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

54. periodic solution

· limited

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

55. harmonic solution

· limited

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

56. Lyapunov stable solution

· Limited

o Unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

57. Lyapunov stability of solutions

· is limited and the tube

o Unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

58. unstable solution

· tends to minus infinity

o Lyapunov stable

o Limited

o Tends to zero

o A permanent solution

59. unstable solution

· tends to plus infinity

o Lyapunov stable

o Limited

o Tends to zero

o A permanent solution

60. harmonic solution

· periodic

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

61. periodic solution

· harmonic

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

62. Solution is Lyapunov stable if

· positive definite Lyapunov function and its derivative is non-positive definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is negative definite

o negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

63. Solution is asymptotically stable if

· positive definite Lyapunov function and its derivative is negative definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is non-positive definite

o non-negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

64. Lienard equation has a solution if the damping rate is less than or equal to zero,

· periodic or an unlimited

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

65. Lienard equation has a solution if the damping rate is greater than or equal to zero,

· periodic or tends monotonically to zero

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

66. Lienard equation has a solution if the damping rate is greater than or equal to zero,

· periodic or tends monotonically to zero

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

67. Lienard equation has zero equilibrium state, if the damping rate is greater than zero,

· tends to zero for any initial conditions

o periodic or tends monotonically to zero

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

68. Lienard equation has zero equilibrium state, if the damping rate is greater than or equal to zero,

· Lyapunov stable

o tends to zero for any initial conditions

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

69. Lienard equation has zero equilibrium state, if the damping rate is greater than zero

· is asymptotically stable in the whole

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

70. Lienard equation is, if the criterion of Bendixson

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

71. Lienard equation is, unless the criterion of Bendixson

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

72. Lienard equation is, if the equation of the contact curve is zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

73. Lienard equation is, if the equation of the curve of contact is not zero,

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

74. Duffing equation has zero equilibrium state, if the coefficients a and b is greater than zero,

· tends to zero for any initial conditions

o periodic or tends monotonically to zero

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

75. Duffing equation has zero equilibrium state, if the coefficients a and b is greater than zero,

· is asymptotically stable in the whole

o periodic or tends monotonically to zero

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

76. Duffing equation has zero equilibrium state, if the coefficients are greater than zero and less than zero,

· Is asymptotically stable

o periodic or tends monotonically to zero

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

77. Duffing equation has zero equilibrium state, if the coefficients a and b is less than zero,

· is unstable

o periodic or tends monotonically to zero

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

78. Lienard equation solution is Lyapunov stable if

· positive definite Lyapunov function and its derivative is non-positive definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is negative definite

o negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

79. Lienard equation solution is asymptotically stable if

· positive definite Lyapunov function and its derivative is negative definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is non-positive definite

o non-negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

80. Duffing equation solution is Lyapunov stable if

· positive definite Lyapunov function and its derivative is non-positive definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is negative definite

o negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

81. Duffing equation solution is asymptotically stable if

· positive definite Lyapunov function and its derivative is negative definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is non-positive definite

o non-negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

82. Rayleigh equation solution is Lyapunov stable if

· positive definite Lyapunov function and its derivative is non-positive definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is negative definite

o negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

83. Rayleigh equation solution is asymptotically stable if

· positive definite Lyapunov function and its derivative is negative definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is non-positive definite

o non-negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

84. Decision van der Pol equation is Lyapunov stable if

· positive definite Lyapunov function and its derivative is non-positive definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is negative definite

o negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

85. Decision van der Pol equation is asymptotically stable if

· positive definite Lyapunov function and its derivative is negative definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is non-positive definite

o non-negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

 

86. Van der Pol equation is, if the criterion of Bendixson

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

87. Van der Pol equation is, unless the criterion of Bendixson

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

88. Van der Pol equation is, if the equation of the contact curve is zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

89. Van der Pol equation is, if the equation of the curve of contact is not zero,

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

90. Lienard equation is, if the criterion of Bendixson

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

91. Lienard equation is, unless the criterion of Bendixson

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

92. Lienard equation is, if the equation of the contact curve is zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

93. Lienard equation is, if the equation of the curve of contact is not zero,

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

94. Rayleigh equation is, if the criterion of Bendixson

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

95. Rayleigh equation is, unless the criterion of Bendixson

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

96. Rayleigh equation is, if the equation of the contact curve is zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

97. Rayleigh equation is, if the equation of the curve of contact is not zero,

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

98. Van der Pol equation is if epsilon zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

99. Van der Pol equation is if epsilon is not zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

100. Equation Duffing has, if the coefficients a and b are equal to zero,

· limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

101. Van der Pol equation is if the coefficients a and b are not equal to zero,

· there is no limit cycle

o periodically or unlimited

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

102. If the coefficients a and b is greater than zero, the Duffing equation has a fixed point

· 1

o 2

o 3

o 4

o 5

103. If the coefficients are greater than zero and less than zero, the Duffing equation has a fixed point

· 3

o 2

o 1

o 4

o 5

104. If the restoring force is not equal, then the equation has a fixed point Lienard

· 1

o 2

o 3

o 4

o 5

105. If the restoring force is not equal, then the equation has a fixed point of the Rayleigh

· 1

o 2

o 3

o 4

o 5

106. If the restoring force is equal to zero for a finite number of x, the Rayleigh equation has a fixed point

· more than one

o the imaginary

o integrated

o a countable set

o countless

107. If the restoring force is equal to zero for a finite number of x, then the equation has a fixed point Lienard

· more than one

o the imaginary

o integrated

o a countable set

o countless

108. If the coefficients a and b is greater than zero, the Duffing equation has a fixed point

· Focus

o Seat

o Node

o Center

o Other types of points

109. If the coefficients are greater than zero and less than zero, the Duffing equation has a fixed point

· focus and saddle

o node and saddle

o center and saddle

o center and saddle

o the focus and center

110. If the coefficients a and b are zero, the Duffing equation has a fixed point

· Center

o node and saddle

o center and saddle

o saddle and saddle

o the focus and focus

111. If all the coefficients are zero, then the equation has a fixed point Lienard

· Center

o node and saddle

o center and saddle

o saddle and saddle

o the focus and focus

112. If all the coefficients are zero, the Rayleigh equation has a fixed point

· Center

o node and saddle

o center and saddle

o saddle and saddle

o the focus and focus

113. If all the coefficients are zero, then the equation has a fixed point Lienard

· Center

o node and saddle

o center and saddle

o saddle and saddle

o the focus and focus

114. If epsilon is zero, the van der Pol equation has a fixed point

· Center

o node and saddle

o center and saddle

o saddle and saddle

o the focus and focus

115. If the criterion of Routh- Hurwitz

· negative roots of the characteristic equation

o roots of different signs

o zero roots

o complex roots

o imaginary roots

116. If the criterion of Routh- Hurwitz

· the real part of the roots of the characteristic equation is negative

o roots of different signs

o zero roots

o complex roots

o imaginary roots

117. If the criterion of Routh- Hurwitz

· negative eigenvalues

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

118. If the criterion of Routh- Hurwitz

· the real part of the eigenvalues ​​of the matrix is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

119. If the criterion of Routh- Hurwitz

· negative eigenvalues ​​of the Jacobi matrix

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

120. If the criterion of Routh- Hurwitz

· the real part of the eigenvalues of the Jacobian matrix is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

121. The criterion of Routh- Hurwitz if

· the principal minors of Hurwitz is greater than zero

o the principal minors of Hurwitz is less than zero

o the principal minors of Hurwitz greater than or equal to zero

o the principal minors of Hurwitz less than or equal to zero

o the principal minors are non-zero Hurwitz

122. If the solution of the Lyapunov equation is symmetric positive definite matrix,

· linear system is asymptotically stable

o the linear system is asymptotically unstable

o the linear system Lyapunov stable

o the linear system is unstable

o linear system is unstable Lyapunov

123. Hurwitz matrix A if

· the real part of the eigenvalues ​​is negative

o the eigenvalues ​​of different signs

o zero eigenvalues

o the complex eigenvalues

o imaginary eigenvalues

124. Hurwitz polynomial if

· the real part of the roots of negative

o roots of different signs

o zero roots

o complex roots

o imaginary roots

125. Solow model has a fixed point

· 3

o 5

o 6

o 7

o 4

126. Solow has

· two nodes and saddle

o two nodes and the center

o two nodes and focus

o two foci and node

o two saddles and focus

127. The decision of the Solow model is asymptotically stable if

· positive definite Lyapunov function and its derivative is negative definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is non-positive definite

o non-negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

128. The decision of the Solow model is Lyapunov stable if

· positive definite Lyapunov function and its derivative is non-positive definite

o positive definite Lyapunov function and its derivative is positive definite

o positive definite Lyapunov function and its derivative is negative definite

o negative definite Lyapunov function and its derivative is positive definite

o negative definite Lyapunov function and its derivative is negative definite

129. Lienard equation solution is unstable if

· Lyapunov function and its derivative have the same sign

o the Lyapunov function and its derivative with different signs

o the Lyapunov function and its derivative is undefined characters

o the Lyapunov function and its derivative is undefined

o the Lyapunov function and its derivative Found

130. Rayleigh equation solution is unstable if

· Lyapunov function and its derivative have the same sign

o the Lyapunov function and its derivative with different signs

o the Lyapunov function and its derivative is undefined characters

o the Lyapunov function and its derivative is undefined

o the Lyapunov function and its derivative Found

131. Duffing equation solution is unstable if

· Lyapunov function and its derivative have the same sign

o the Lyapunov function and its derivative with different signs

o the Lyapunov function and its derivative is undefined characters

o the Lyapunov function and its derivative is undefined

o the Lyapunov function and its derivative Found

132. Solution of the equation Solow unstable if

· Lyapunov function and its derivative have the same sign

o the Lyapunov function and its derivative with different signs

o the Lyapunov function and its derivative is undefined characters

o the Lyapunov function and its derivative is undefined

o the Lyapunov function and its derivative Found

133. Decision van der Pol equation is unstable if

· Lyapunov function and its derivative have the same sign

o the Lyapunov function and its derivative with different signs

o the Lyapunov function and its derivative is undefined characters

o the Lyapunov function and its derivative is undefined

o the Lyapunov function and its derivative Found

134. stable node

· bounded solution

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

135. stable node

· bounded solution and tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

136. stable node

· tends to zero for the end of the initial conditions

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

137. stable node

· tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

138. stable node

· tends to zero for any initial conditions

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

139. stable focus

· bounded solution

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

140. stable focus

· bounded solution and tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

141. stable focus

· tends to zero for the end of the initial conditions

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

142. stable focus

· tends to zero

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

143. stable focus

· tends to zero for any initial conditions

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

144. limit cycle

· bounded solution and periodic

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

145. limit cycle

· bounded solution and harmonic

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

146. limit cycle

· periodic

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

147. limit cycle

· harmonic and bounded

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

148. limit cycle

· limited solution with period

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

149. Closed curve is

· bounded solution and periodic

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

150. Closed curve is

· bounded solution and harmonic

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

151. closed curve is

· periodic

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

152. closed curve is

· harmonic and bounded

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

153. closed curve is

· limited solution with period

o unstable Lyapunov

o tends to minus infinity

o tends to plus infinity

o an unstable periodic solution

 


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