Abstract
This paper introduces a new chaotic system with two circles of equilibrium points. The dynamical properties of the proposed dynamical system are investigated through evaluating Lyapunov exponents, bifurcation diagram and multistability. The qualitative study shows that the new system exhibits coexisting periodic and chaotic attractors for different values of parameters. The new chaotic system is implemented in both analog and digital electronics. In the former case, we introduce the analog circuit of the proposed chaotic system with two circles of equilibrium points using amplifiers, which is simulated in MultiSIM software, version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB. In addition, we perform the digital implementation of the new chaotic system using field-programmable gate arrays (FPGA), the experimental observations of the attractors of which confirm its suitability to generate chaotic behavior.
Highlights
A nonlinear, aperiodic and continuous-time dynamical system is said to be chaotic if it exhibits sensitive dependence on initial conditions [1]
Pham et al proposed a new chaotic system with equilibria located on the rounded square loop and discussed its circuit implementation [6]
We propose a new chaotic system with two circles of equilibrium points
Summary
A nonlinear, aperiodic and continuous-time dynamical system is said to be chaotic if it exhibits sensitive dependence on initial conditions [1]. Pham et al proposed a new chaotic system with equilibria located on the rounded square loop and discussed its circuit implementation [6]. Sambas et al proposed a new chaotic system with pear-shaped equilibrium and discussed its electronic circuit simulation [8]. Proposed a new chaotic system with axe-shaped equilibrium and discussed its control applications [9]. Vaidyanathan et al proposed a new chaotic system with a cloud-shaped curve of equilibrium and discussed its application to sound encryption [10]. Mobayen et al announced a new chaotic system with a boomerang-shaped equilibrium and discussed its application to sound encryption [11]. The electronic circuit of the proposed chaotic system with two circles of equilibrium points is implemented in MultiSIM software, version 13.0. FPGA circuit design has several applications in engineering [17]
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