An Offset-Boostable Chaotic Oscillator with Broken Symmetry

Abstract

A new 3D offset-boostable symmetric system is proposed by an absolute value function introduced. The system seems to be more fragile and easier to the state of broken symmetry. Coexisting symmetric pairs of attractors get closer and closer, and finally get emerged together. Basins of attraction show how these coexisting attractors are arranged in phase space. All these coexisting attractors can be easily offset boosted in phase space by a single constant when the initial condition is revised accordingly. PSpice simulations prove all the phenomena.

A New DC Offset Boostable Chaotic System with Multistability, Coexisting Attractors and Its Adaptive Synchronization

“…In the recent years, the offset boosting of chaotic signals has become an active area of research in chaotic literature and many scholars have applied the method to their proposed chaotic systems. In some of the systems [55][56][57][58][59], both initial conditions triggered coexisting attractors and offset boosting coexisting attractors have been realized.…”

Multistability Dynamics Analysis and Digital Circuit Implementation of Entanglement-Chaos Symmetrical Memristive System

“…Since then, many scholars have devoted themselves to the research of memristors, and it has become a research hotspot in many fields such as circuit and computer science [3,4]. Many scientists have found that embedding memristors into analog circuits can easily lead to complex oscillation behaviors such as chaos [5][6][7][8][9][10], the multistable attractor of the Chua memristive system [10][11][12][13], regulation and control of attractors [14,15], no equilibrium point or stable equilibrium point of systems [16][17][18][19][20], and high-dimensional systems [21]. Some scholars have also studied discrete memristor chaotic systems [22].…”

“…In recent years, the research of memristor circuits, hidden attractors, and multistability has become a hot topic in the direction of nonlinear chaos dynamics [10][11][12][13][14][15]23]. Multistability means that the phase diagram of the system shows the coexistence of multiple attractors when the initial conditions of the nonlinear chaotic system are changed without changing any other parameters.…”