A Novel Chaotic Attractor With a Line and Unstable Equilibria: Dynamics, Circuit Design, and Microcontroller-Based Sliding Mode Control

Abstract

This study proposes a novel chaotic attractor with seven terms in three simple ordinary differential equations involving a line and unstable equilibria. The complex dynamical behavior of the proposed system is studied in detail by analyzing its equilibria, Lyapunov spectra, and bifurcation diagram. The feasibility and accuracy of the novel attractor are examined by constructing its analog circuit implementation. Additionally, periodic states of the system are examined in both numerical and PSpice simulations, as well as an analog circuit implementation. The hardware experimental results are highly compatible with numerical and PSpice simulations. As can be seen from the numerical simulations and hardware implementation, the presented system shows sensitive and rich dynamic behaviors in a small range of system parameters. The proposed oscillator circuit is also cost-effective, as it has only seven terms. Additionally, a sliding mode controller (SMC) is presented to control the novel attractor. The stability of the designed SMC is proven via the Lyapunov stability method. Lastly, a microcontroller-based implementation is realized, and it is seen that the experimental results are in good accordance with the simulation results. The correctness of the proposed controller is approved by theoretical analysis, numerical simulations, and experimental results.