A method of targeting synchronization and its control is reported in chaotic oscillators. This proposes design of appropriate coupling using an open-plus-closed-loop (OPCL) scheme based on Hurwitz stability to establish a desired state of synchrony between the oscillators. In the synchronization state, a chaotic attractor can be scaled up or down in size relative to another attractor. Additiona...

We propose a discrete time dynamical system (a map) as a phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find conditions under which this map has an invariant region on the phase plane, containing a chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of o...

A new design of a hysteresis chaotic circuit is proposed. The simple circuit consists of one capacitor, one inductor, one resistor (negative) and one hysteresis VCVS. Computer simulation results, showing the existence of the double scroll attractor, are reported. Key-Words: Chaos, chaotic circuit, hysteresis, attractor, bifurcation, oscillator 1 This work was supported by the Louisiana BORSF co...

A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independant parameters which are uniquely determined by the underlying process that generates the attractor. The method maps the f(α) spectrum of a chaotic attractor onto that of a general two scale Cantor measure....

Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable pe...

A simple approach to the creation of a strange nonchaotic attractor in any chaotic system is described. The main idea is to control the parameter of the system in such a manner that the system dynamics is expanding at some times, but converging at others. With this approach, a strange nonchaotic attractor can be found in a large region in the parameter space near the boundaries between chaotic ...

Controlling chaos has become a challenging topic in nonlinear dynamics. It has been studied in many scientific and engineering fields such as physics, chemistry, electrical circuit, etc., and several extension and applications of the original OGY control method [1] have been reported [2–6]. Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [7]. Recent r...

We analyze a model of a chaotic neural network consisting of three neurons, namely a chaotically forcing neuron and two neurons comprizing a stable response system with a contraction mapping property, for digital encoding with chaotic dynamics. We show that dynamics of the chaotically forcing neuron is embedded in the form of a code sequence on a fractal attractor of the two-neuron response sys...

A first-order delayed chaotic model with n-double scroll attractors is investigated. The associated piecewise-linear activation function requires only a few operational amplifiers, which can easily be realized by an electronic circuit. The typical waveforms and phase portraits are plotted to illustrate n-double scroll chaotic oscillations. Keywords—delay; chaotic attractor; n-double scroll; cir...