Labyrinth chaos: revisiting the elegant, chaotic, and hyperchaotic walks. (English) Zbl 1460.37035
The authors start by recalling the notion of Rössler-Thomas circuits and the occurence of chaos and hyperchaos in dynamical systems.
Then the dynamics in the neighborhood of the fixed points of labyrinth walks is described. In addition, it is presented how there can exist chaos and hyperchaos in absence of attractors. They consider the system given by \[\dot x_1=\sin x_2~, ~\dot x_2=\sin x_3~,~ \dot x_3=\sin x_1.\tag{1}\] as illustrative example. Section 4 deals with a system of coupled 3D labyrinth walk and Thomas-Rössler systems arranged in a simple ring topology with nonlocal coupling. Furthermore, the role of labyrinth walks in the emergence of chimera-like states is highlighted.
In Section 5, it is proved that system (1) is volume-preserving, but it is not force-conservative. As the authors claim, “this makes it a fine and elegantly simple example of a low-dimensional volume-preserving, chaotic system with no attractors and with only unstable fixed points.”
In Section 6, possible future directions of work are discussed.
In Section 5, it is proved that system (1) is volume-preserving, but it is not force-conservative. As the authors claim, “this makes it a fine and elegantly simple example of a low-dimensional volume-preserving, chaotic system with no attractors and with only unstable fixed points.”
In Section 6, possible future directions of work are discussed.
Reviewer: Cristian Lăzureanu (Timişoara)
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
| 94C05 | Analytic circuit theory |
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