Abstract
This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.
Highlights
Encouraging progress has been made on chaos in the past few decades
E most representative work was made by Sprott who established nineteen polynomial chaotic systems with either five terms and two nonlinear terms or six terms and one nonlinear term [8]. e other is to construct chaotic systems with special strange attractors including butterfly attractor, multiscroll attractor, multiwing attractor, hidden attractor, and coexisting attractors [9,10,11,12,13,14]. e number and type of equilibria play a decisive role in the dynamic properties of chaotic system to some extent
A classic argument is that a dynamic system with one saddle focus connected by homoclinic orbit or two saddle foci connected by heteroclinic orbit generates horseshoe chaos [15]
Summary
Encouraging progress has been made on chaos in the past few decades. An important change is to recognize the great application potential of chaos in engineering. E attractors produced by this method usually have the same properties Another interesting question is how many nontrivial attractors can be coexist in phase space of nonlinear system, which corresponds to a chaotic generalization [34] of the second part of Hilbert’s 16th problem. E phenomenon of coexisting attractors that corresponds to the generation of multiple attractors with independent basins of attractions implies the strong influence of initial conditions on the final state of system Both hidden attractors and coexisting attractors are interesting nonlinear dynamics worthy of further study. This paper aims to present a new autonomous chaotic system with infinitely many coexisting hidden attractors from the perspective of building complex behavior of simple system.
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