Chaos Entanglement: Leading Unstable Linear Systems to Chaos.

Chaos entanglement is a new approach to connect linear systems to chaos. The basic principle is to entangle two or multiple linear systems by nonlinear coupling functions to form an artificial chaotic system/network such that each of them evolves in a chaotic manner. However, it is only applicable for stable linear systems, not for unstable ones because of the divergence property. In this study, a bound function is introduced to bound the unstable linear systems and then chaos entanglement is realized in this scenario. Firstly, a new 6-scroll attraetor, entangling three identi-cal unstable linear systems by sine function, is presented as an example. The dynamical analysis shows that all entangled subsystems are bounded and their equilibrium points are unstable sad-dle points when chaos entanglement is achieved. Also, numerical computation exhibits that this new attraetor possesses one positive Lyapunov exponent, which implies chaos. Furthermore, a 4 x 4 x 4-grid attraetor is generalized by introducing a more complex bound function. Hybrid entanglement is obtained when entangling a two-dimensional stable linear subsystem and a one-dimensional unstable linear subsystem. Specifically, it is verified that it is possible to produce chaos by entangling unstable linear subsystems through linear coupling functions -- a special approach referred to as linear entanglement. A pair of 2-scroll chaotic attractors are established by linear entanglement. Our results indicate that chaos entanglement is a powerful approach to generate chaotic dynamics and could be utilized as a guideline to effectively create desired chaotic systems for engineering applications. [ABSTRACT FROM AUTHOR]