Simulation and experimental validation of a non-equilibrium chaotic system

Abstract Nowadays, chaotic systems are attracting considerable attention due to their special features. The aim of this paper is to study a four-dimensional system that lacks any equilibria. Also, this non-equilibrium system has hidden attractors. Dynamical behaviors of the system have been investigated using well-known numerical simulations and analyses such as phase portraits, Poincare maps, Lyapunov exponents, bifurcation diagrams, and basins of attraction. This way, the chaotic behavior in the system is verified. In addition, the chaotic behavior of the system has been studied by designing and implementing a real-time analog circuit. The circuitry implementation of the system is presented, and the dynamical behaviors of the system have been empirically demonstrated. To characterize the circuit an automatic routine through LabView has been developed in which by increasing a parameter of the system the bifurcation diagram has been obtained and depicted. A DAQ 6363 storing temporal series of one second to posteriory has been used to acquire the data and analyze such information. Experimental results clearly illustrate the chaotic behavior of the system. Also, the presented experimental results pave the way for using the proposed system in possible engineering applications such as data transmission and information security.