A 4D chaotic system with seventeen equilibria: Synchronization and anti-synchronization

摘要

This paper puts forward a 4D autonomous chaotic system, synchronisation and anti-synchronisation using nonlinear active control technique. The 4D chaotic system is analyzed by using available qualitative and quantitative tools like phase plane analysis, time series plot, root locus, Lyapunov exponent and spectrum analyses. The proposed 4D chaotic system has seventeen equilibria and coexisting attractors of two and single wings and shows symmetric phase plane behaviour with respect to origin and coordinate plane. The proposed 4D autonomous dynamic system reflects sensitive dependence on initial conditions and exploring different types of synchronisation between 4D chaotic systems is a challenging task. Synchronisation and anti-synchronisation between proposed 4D chaotic systems are accomplished using nonlinear active control technique. Control laws are designed by employing sum of pertinent variables of 4D drive and response chaotic systems. Lyapunov direct stability theorem is used and global asymptotic stability condition is derived to confirm the stability of error dynamics. Simulation is finished in MATLAB environment and reveals the accomplishment of objectives.