A new time-reversible 3D chaotic system with coexisting dissipative and conservative behaviors and its active non-linear control

Abstract

Most of the explored chaotic systems are either of dissipative or conservative behavior. The dissipative or conservative behavior of a chaotic system is governed by its divergence of volume. The system shows a dissipative nature for negative divergence whereas for zero divergence, a conservative nature is shown by the system. In most of the literature, these behaviors are shown in a chaotic system either with the change in system parameters or with the initial conditions. However, a chaotic system that can show both dissipative and conservative behavior based on the initial conditions and also on the system parameters is rare in the literature. Therefore, a novel chaotic system is proposed that can meet such peculiarities. In addition, the proposed system also possesses attractors of self-excited and hidden nature. The system is developed by using a Hamiltonian approach of modifying the skew-symmetric matrix and adjusting the rest of the system parameters to control the system divergence. The proposed system boasts the presence of heterogeneous multistability, extreme multistability and the coexistence of conservative flow and dissipative attractor. Many qualitative inspections are done using phase portraits, Lyapunov spectrums, bifurcation diagrams and Poincare maps to support the claims. Further, to demonstrate the controllability of the chaotic system a nonlinear active controller with single control input is designed. The real-time application of the proposed system is validated by the circuit simulation in NI Multisim and hardware implementation on a Arduino board.