Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley...

Feigenbaum discovered a pattern in the period doubling route to chaos for nonlinear systems whose first return map is unimodal with a quadratic extremum. This led to the definition of the Feigenbaum universal constant δ. This constant could then be used to predict the parameter value for which such nonlinear systems turn chaotic, that is, the parameter value (P∞) for which the period tends to i...

In recent years, a growing number of cryptosystems based on chaos have been proposed. The majority of them are based on parameter modulation of a chaotic oscillator being the transmitter while the receiver is also a chaotic system synchronized by means of an adaptive observer. For example, a Lorenz’s attractor is used as the non-linear time-varying system while the encryption process modulates ...

This article discusses the multispiral Chua Chaotic attractor’s hidden bifurcations that are generated by sine function. The number of spirals (also known as a multiscroll attractor) controlled integer parameter c can be used to describe basic shape chaotic attractors. Since this is an integer, increasing it one does not allow observation from n + 2 spirals. method bifurcations, however, enable...

We report our results on non-periodic experimental time series of pressure in a spark ignition engine. The experiments were performed for a low rotational velocity of a crankshaft and a relatively large spark advance angle. We show that the combustion process has many chaotic features. Surprisingly, the reconstructed attractor has a characteristic butterfly shape similar to a chaotic attractor ...

We propose a method for designing chaos generators. We introduce a switched system with three-dimensional space functions for generating a new type of chaotic attractor, and then we introduce saturated function series for generating n-scroll chaotic attractor. Moreover, we present some examples with numerical simulations that illustrate the efficiency of ourmethod. The statistic behavior is als...

The Cournot triopoly model may possess a triple chaotic attractor. In the paper, we present an approach for controlling the three coexisting chaotic attractors by means of steering the system dynamics from one attractor to another. The control scheme is based on predictive control. We give the design procedure and show by numerical results the effectiveness of the control in presence of the inp...