Circuit Realization of a 3D Multistability Chaotic System and Its Synchronization via Linear Resistor and Linear Capacitor in Parallel Coupling

In this paper, a 3D multistability chaotic system with two coexisting conditional symmetric attractors is studied by using a circuit block diagram and realized by using an electronic circuit. The simulation results show that two coexisting conditional symmetric attractors are emerged in this electronic circuit. Furthermore, synchronization of this 3D multistability chaotic system and its electronic circuit is studied. It shows that linear resistor and linear capacitor in parallel coupling can achieve synchronization in this chaotic electronic circuit. That is, the output voltage of chaotic electronic circuit is coupled via one linear resistor and one linear capacitor in parallel coupling. The simulation results verify that synchronization of the chaotic electronic circuit can be achieved.

True Random Source from Integratable Chaotic Circuits

In this talk, we describe a chaotic electronic circuit designed to realize a physical random number generator that is easily integrated. The small footprint of the circuit enables massive parallel realization to achieve high-speed, true-random bit sequences. The analog circuit can be fully characterized, and conjugacy to a symbolic shift proves the presence of chaos. The symbolic representation also provides a rigorous means to extract the maximum entropy from the chaotic device. Analysis of the circuit dynamics reveals critical tunings that yield special Markov properties, which are essential for removing correlations in the random sequences. Practically important is the presence of a sensitive circuit statistic that enables efficient feedback control to the Markov tuning. Numerical simulation and breadboard experimental results demonstrate the effectiveness of the proposed physical random number generator device.

THEORY AND EXPERIMENT OF A FIRST-ORDER CHAOTIC DELAY DYNAMICAL SYSTEM

We report the theory and experiment of a new time-delayed chaotic (hyperchaotic) system with a single scalar time delay and a nonlinearity described by a closed form mathematical function. Detailed stability and bifurcation analyses establish that with the suitable delay and system parameters, the system shows a stable limit cycle through a supercritical Hopf bifurcation. Numerical simulations exemplify that the system depicts mono-scroll and double-scroll chaos and hyperchaos for a range of delay and other system parameters. Nonlinear behavior of the system is characterized by Lyapunov exponents and Kaplan–Yorke dimension. It is established that, for some suitably chosen system parameters, the system shows hyperchaos even for a small or moderate time delay. Finally, the system is implemented in an analogue electronic circuit using off-the-shelf circuit elements. It is shown that the behavior of the time delay chaotic electronic circuit qualitatively agrees well with our analytical and numerical results.

MEMRISTIVE CHAOTIC CIRCUITS BASED ON CELLULAR NONLINEAR NETWORKS

Memristors are gaining increasing interest in the scientific community for their possible applications, e.g. high-speed low-power processors or new biological models for associative memories. Due to the intrinsic nonlinear characteristic of memristive devices, it is possible to use them in the design of new dynamical circuits that are able to show complex behavior, like chaos. In this paper, two new memristive chaotic circuits are presented discussing, in particular, an approach based on Cellular Nonlinear Networks for the implementation of the memristive device. The approach investigated in this paper allows to obtain memristors with common off-the-shelf components and to observe the onset of new chaotic attractors in nonlinear circuits with memristors. Furthermore, the circuits presented in this paper, being the first examples of memristive chaotic circuits based on CNNs, can be considered as the link between the three inventions by Leon O. Chua, i.e. the memristor, the first chaotic electronic circuit and Cellular Nonlinear Networks.

A universal circuit for studying chaotic phenomena

In this paper, an overview of the results on an autonomous chaotic electronic circuit, called Chua’s oscillator, is given. Along with brief descriptions of numerical and analytical investigations on Chua’s oscillator, we present some of its potential applications. The significance of the oscillator for the study of general dynamical systems is discussed.

STOCHASTIC RESONANCE IN CHUA’S CIRCUIT

In this paper, we report numerical observations of the stochastic resonance (SR) phenomenon in a bistable chaotic electronic circuit (namely, Chua’s circuit) driven simultaneously by noise and a sinusoidal signal. It is shown that the noise-induced “chaos-chaos” type intermittency is a physical mechanism of the SR-phenomenon in chaotic systems. The resulting amplification of the sinusoidal signal intensity is due to a coherent interaction of three characteristic frequencies of the system. The SR-phenomenon can be controlled by a variation of either the noise intensity or the system parameters in the absence of noise.