Novel Pehlivan–Uyarŏglu Chaotic System Variants and their CFOA Based Realization

Abstract

In this paper, four variants of Pehlivan–Uyarŏglu chaotic system (PUCS) have been proposed. The properties of the proposed PUCSs are examined through numerical simulations and the parameter values are obtained by observing the bifurcation diagrams for state variables. Further, the convergence/divergence of nearby orbits is investigated by noticing the evolution of Lyapunov exponents with time. It is found that the values of Lyapunov exponents are negative, zero and positive for all proposed variants thus confirming the chaoticity of the proposals. The strangeness of the proposed variants is also studied. The stability of PUCS and its proposed variants is examined using Jacobi stability analysis. A current feedback operational amplifier (CFOA) based circuit is put forward that can realize the existing PUCS and its proposed variants, by simply adjusting the component values. The proposed realization is compact (23% saving in overall component count) in comparison to its operational amplifier (OpAmp) based counterpart. The behavior of the proposed variants in time domain, frequency domain and phase space have been examined through simulations in LTspice design environment. Furthermore, the feasibility of the proposed variants is also discussed through presenting the electronic circuit implementation of two of the variants and the results obtained are in good agreement with the LTspice simulations. Monte Carlo (MC) simulations are also included to show the robustness of the proposed circuit against parameter variations.