Slideset () - Journal of Computational and Nonlinear Dynamics

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Slideset () - Journal of Computational and Nonlinear Dynamics
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
The figure of the first Lyapunov exponent l1. It implies that the values of l1(b, c) can be positive, zero, and negative when (a,b,c)
S212.
∈
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Two orbits of system (7) for time integration: [0, 250], the initial conditions: (a) (x0,y0,z0)=(0,±3.82 × 10-5,±6.18 × 10-5), (b)
(x0,y0,z0)=(1,±3.82 × 10-5,±6.18 × 10-5) and the parameters: a = 0, b = 1 and c = 2, which imply the existence of two
singularly degenerate heteroclinic cycles of system (7)
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Degenerate heteroclinic cycles of system (7) with (a) (x0,y0,z0)=(-2,±3.82 × 10-5,±6.18 × 10-5), (b) (x0,y0,z0)=(0,±3.82 ×
10-5,±6.18 × 10-5), and (c) (x0,y0,z0)=(2,±3.82 × 10-5,±6.18 × 10-5) when (a,b,c)=(0,2,5). This figure suggests that
system (7) has infinitely many degenerate heteroclinic cycles.
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Phase portraits of system (7) for the parameters b = 2, c = 3 and (a) a = 0, (b) a = 0.07, time of integration: [0, 250], and the initial
conditions: (x0,y0,z0)=(0,±3.82 × 10-5,±6.18 × 10-5), implying the existence of chaotic attractors bifurcated from the
singularly degenerate heteroclinic cycles of system (7)
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Two homoclinic orbits of system (7) to E0 as t→±∞ for a = 3.27, b = 2, c = 3 and different initial values: (a) (x0,y0,z0)=(0,3.82
5,6.18 × 10-5) and (b) (x0,y0,z0)=(0,-3.82 × 10-5,-6.18 × 10-5)
×
10-
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Two orbits of system (7) for time integration: [0, 2000], the initial conditions: (x0,y0,z0)=(0,±3.82 × 10-5,±6.18 × 10-5) and
the parameters: (b,c)=(1,7) and a satisfying a > 0((a,b,c) ∈ S214): (a) a = 0.01, (b) a = 0.07, (c) a = 0.7, and (d) a = 3, implying the
existence of two heteroclinic orbits of system (7) joining E0 and E±, respectively
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Phase portraits of system (7) when (x0,y0,z0)=(0,±3.82×10-5,±6.18×10-5) and (a) (a,b,c)=(3.9,2,3), (b) (a,b,c)=(500,2,3), which
illustrate that system (7) has two heteroclinic orbits to E0 and E± when (a,b,c)∈S213
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Phase portrait of system (7) at infinity
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Phase portrait of the first integral H1=(z12+z2)/(1+z22)+arctanz2 for different H 1, where black orbits mean H1
to H1=0, and green orbits point toward H1 < 0
>
0, red orbit refers
Date of download: 8/12/2017
Copyright © ASME. All rights reserved.
From: New Results to a Three-Dimensional Chaotic System With Two Different Kinds of Nonisolated Equilibria
J. Comput. Nonlinear Dynam. 2015;10(6):061021-061021-14. doi:10.1115/1.4030028
Figure Legend:
Phase portrait of the first integral H2=(z12+z2)/(1+z22)-arctanz2 for different H2, where black orbits mean H2
to H2=0, and green orbits point toward H2 < 0
>
0, red orbit refers

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