Dynamic analysis and electronic circuit implementation of a novel 3D autonomous system without linear terms

作者：Kengne J^*; Jafari S; Njitacke Z T; Khanian M Yousefi Azar; Cheukem A

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 52: 62-76.

DOI：10.1016/j.cnsns.2017.04.017

• Chaotic system without linear terms
• Bifurcation analysis
• Period-doubling route to chaos
• Antimonotonicity
• Pspice simulation

Mathematical models (ODEs) describing the dynamics of almost all continuous time chaotic nonlinear systems (e.g. Lorenz, Rossler, Chua, or Chen system) involve at least a nonlinear term in addition to linear terms. In this contribution, a novel (and singular) 3D autonomous chaotic system without linear terms is introduced. This system has an especial feature of having two twin strange attractors: one ordinary and one symmetric strange attractor when the time is reversed. The complex behavior of the model is investigated in terms of equilibria and stability, bifurcation diagrams, Lyapunov exponent plots, time series and Poincare sections. Some interesting phenomena are found including for instance, period-doubling bifurcation, antimonotonicity (i.e. the concurrent creation and annihilation of periodic orbits) and chaos while monitoring the system parameters. Compared to the (unique) case previously reported by Xu and Wang (2014) [31], the system considered in this work displays a more 'elegant' mathematical expression and experiences richer dynamical behaviors. A suitable electronic circuit (i.e. the analog simulator) is designed and used for the investigations. Pspice based simulation results show a very good agreement with the theoretical analysis.

• 出版日期2017-11