A chaotic flow has an involutional symmetry if the form of the dynamical equations remains unchanged when one or more of the variables changes sign. Such systems are of theoretical and practical importance because they can exhibit symmetry breaking in which a symmetric pair of attractors coexist and merge into one symmetric attractor through an attractor-merging bifurcation. This paper describe...

The presence of part-through cracks with limited length is one of the prevalent defects in the plate structures. Due to the slight effect of this type of damages on the frequency response of the plates, conventional vibration-based damage assessment could be a challenging task. In this study for the first time, a recently developed state-space method which is based on the chaotic excitation is ...

Spiral-wave breakup in strongly chaotic media with nonphase-coherent chaotic attractors is investigated. Spiral-wave dynamics is studied for the Rössler reaction diffusion equation as the local attractor changes from a phase-coherent to a funnel form. Stable spiral waves with an Archimedean structure are observed to persist even when the local chaotic attractor has a funnel form. The destructio...

which is chaotic on a particular parameter set, (σ, ρ, β) = (10, 28, 8/3)1 in the real parameter space of the general system (1); but for other parameter sets, system (1) may not be chaotic. The chaotic Lorenz system (2) has received sustained research interest in the literature since its discovery. For example, in [Tucker, 1999; Stewart, 2000], a rigorous proof confirms the existence of the ch...

In this paper, a novel three-dimensional autonomous chaotic system is proposed. The proposed system contains four variational parameters, a cubic nonlinearity term (i.e. product of all the three states) and exhibits a chaotic attractor in numerical simulations. The basic dynamic properties of the system are analyzed by means of equilibrium points, Eigen values and Lyapunov exponents. Finally, t...

Results are reported concerning the transition to chaos in random dynamical systems. In particular, situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle, which can be expected in any periodic window of a nonlinear dynamical system. Under noise, the asymptotic attractor of the system can become chaotic, as characterized by the appearance of a positive...

This paper studies synthesis of chaotic oscillators using 2-port VCCSs and capacitors. As a rst step, we design a 4-D hysteresis chaotic oscillator using one linear 2-port VCCS, one hysteresis 2-port VCCS and two capacitors. In the circuit, we have con rmed theoretically that a simple periodic attractor changes into quad screw chaotic attractor as in uence of the nonlinearity decreases.

This paper investigates the global synchronization method of two identical systems and two different chaotic systems. The proposed method is effective and convenient to synchronize two identical systems and two different chaotic systems by using nonlinear control functions. The method has been applied successfully to make two identical four-scroll attractor and also two different chaotic system...

Predicting future behavior of chaotic time series system is a challenging area in the literature of nonlinear systems. The prediction's accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. On the other hand the cyclic solar activity as one of the natural chaotic systems has significant effects on earth, climate, satellites and space missions. Several m...

We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram (EEG). Two limit cycle attractors and one chaotic attractor were found to coexist in a two-dimensional plane of the tendimensional volume of initial conditions. The chaotic attractor was found to have a moderate value of the largest Lyapunov exponent (3.4 s−1 base e) with ∗Correspondin...