Current-Mode Network Structures Dedicated for Simulation of Dynamical Systems with Plane Continuum of Equilibrium

Abstract

This review paper describes di®erent lumped circuitry realizations of the chaotic dynamical systems having equilibrium degeneration into a plane object with topological dimension of the equilibrium structure equals one. This property has limited amount (but still increasing, especially recently) of third-order autonomous deterministic dynamical systems. Mathematical models are generalized into classes to design analog networks as universal as possible, capable of modeling the rich scale of associated dynamics including the so-called chaos. Reference state trajectories for the chaotic attractors are generated via numerical analysis. Since used active devices can be precisely approximated by using third-level frequency dependent model, it is believed that computer simulations are close enough to capture real behavior. These simulations are included to demonstrate the existence of chaotic motion.

A Novel Mega-stable Chaotic Circuit

“…Previous researches have described general methods in order to implement mathematical models using voltage-mode devices [42] and current-mode active elements [10]. It is possible to implement the forced chaotic oscillator (6) by using a circuit [43][44][45][46][47][48][49][50][51] as designed in Fig.…”

“…Recently there has been growing attention in finding chaotic systems with special qualities. Systems with no equilibrium [3], [4], with stable equilibria [5], [6], with curves of equilibria [7][8][9], with surface of equilibria [10][11][12], with multi-scroll attractors [13], with hidden attractors [14], [15], with amplitude control [16], [17], with simplest form , having hyperchaos [18][19][20], having fractional order form [21][22][23], with topological horseshoes [24], [25], and with extreme multistability [26][27][28][29], are examples of them. Another major category of chaotic systems includes periodically-forced nonlinear oscillators [30].…”

Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

“…In that way, we demonstrate the system's feasibility. From the viewpoint of practical applications [62,63] the hardware implementation of a mathematical chaotic model is an important issue, especially if the circuit is realized using commercially available components like amplifiers and integrated circuits [64][65][66].…”

Circuit Equivalent to Rucklidge System

“…Mathematical model (1) can be realized as a current-mode circuit (i.e. state variables are currents) by adopting approach described in [15]. By processing currents instead of voltages, we can move fundamental frequency generated by system toward the upper frequency bounds; probably up to the hundreds of kHz.…”