Mechanisms of strange nonchaotic attractors in a nonsmooth system with border-collision bifurcations

2019 ◽  
Author(s):  
Yunzhu Shen ◽  
Yongxiang Zhang
Keyword(s):  
Nonsmooth System ◽  
Border Collision Bifurcations ◽  
Strange Nonchaotic Attractors

scholarly journals The effect of noise on strange nonchaotic attractors

2000 ◽  
Vol 268 (4-6) ◽  
pp. 315-322 ◽  
Author(s):  
I.A. Khovanov ◽  
N.A. Khovanova ◽  
P.V.E. McClintock ◽  
V.S. Anishchenko
Keyword(s):  
Strange Nonchaotic Attractors

Bifurcations and Chaos in a Minimal Neural Network: Forced Coupled Neurons

2021 ◽  
Vol 31 (10) ◽  
pp. 2150147
Author(s):  
Yo Horikawa
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Period Doubling ◽  
Output Function ◽  
Piecewise Constant ◽  
Border Collision Bifurcations ◽  
Saddle Node ◽  
Periodic Input ◽  
Symmetric Periodic Solution ◽  
Period Doubling Bifurcations

The bifurcations and chaos in a system of two coupled sigmoidal neurons with periodic input are revisited. The system has no self-coupling and no inherent limit cycles in contrast to the previous studies and shows simple bifurcations qualitatively different from the previous results. A symmetric periodic solution generated by the periodic input underdoes a pitchfork bifurcation so that a pair of asymmetric periodic solutions is generated. A chaotic attractor is generated through a cascade of period-doubling bifurcations of the asymmetric periodic solutions. However, a symmetric periodic solution repeats saddle-node bifurcations many times and the bifurcations of periodic solutions become complicated as the output gain of neurons is increasing. Then, the analysis of border collision bifurcations is carried out by using a piecewise constant output function of neurons and a rectangular wave as periodic input. The saddle-node, the pitchfork and the period-doubling bifurcations in the coupled sigmoidal neurons are replaced by various kinds of border collision bifurcations in the coupled piecewise constant neurons. Qualitatively the same structure of the bifurcations of periodic solutions in the coupled sigmoidal neurons is derived analytically. Further, it is shown that another period-doubling route to chaos exists when the output function of neurons is asymmetric.

Strange Nonchaotic Trajectories on Torus

1997 ◽  
Vol 07 (02) ◽  
pp. 423-429 ◽  
Author(s):  
T. Kapitaniak ◽  
L. O. Chua
Keyword(s):  
Lebesgue Measure ◽  
Parameter Space ◽  
Positive Lebesgue Measure ◽  
Strange Nonchaotic Attractors

In this letter we have shown that aperiodic nonchaotic trajectories characteristic of strange nonchaotic attractors can occur on a two-frequency torus. We found that these trajectories are robust as they exist on a positive Lebesgue measure set in the parameter space.

Boundedness of a Class of Complex Lorenz Systems

2021 ◽  
Vol 31 (07) ◽  
pp. 2150101
Author(s):  
Xu Zhang
Keyword(s):  
Dynamical System ◽  
Current Literature ◽  
Chaos Control ◽  
Type Systems ◽  
Chaotic Attractors ◽  
Strange Nonchaotic Attractors ◽  
Control And Synchronization ◽  
Ultimate Bound

The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem. Based on these results, a kind of complex Lorenz-type systems is constructed, which might have many or infinitely many strange nonchaotic attractors, chaotic attractors, or an infinitely-many-scroll attractor.

OLD AND NEW RESULTS ON STRANGE NONCHAOTIC ATTRACTORS

2007 ◽  
Vol 17 (11) ◽  
pp. 3895-3928 ◽  
Author(s):  
ÀNGEL JORBA ◽  
JOAN CARLES TATJER ◽  
CARMEN NÚÑEZ ◽  
RAFAEL OBAYA
Keyword(s):  
Differential Equations ◽  
Topological Structure ◽  
Base Flow ◽  
Skew Products ◽  
Almost Automorphic ◽  
Strange Nonchaotic Attractors

Classical and new results concerning the topological structure of skew-products semiflows, coming from nonautonomous maps and differential equations, are combined in order to establish rigorous conditions giving rise to the occurrence of strange nonchaotic attractors on 𝕋d × ℝ. A special attention is paid to the relation of these sets with the almost automorphic extensions of the base flow. The scope of the results is clarified by applying them to the Harper map, although they are valid in a much wider context.

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