Considering the effect of geometric nonlinearity and uniformly distributed time-varying temperature, the bifurcation behaviors and chaotic phenomena of a bimetallic thin circular plate are investigated. First of all, the nonlinear dynamic equation for bimetallic plate is established and further reduced to Duffing equation of harmonic parametric excitation, from which the pitchfork bifurcation p...

Permutation entropy is a metric used to quantify the regularity of a time series. Here I report on its application to the problem of characterizing the behavior of a few nonlinear dynamical systems, specifically the Duffing oscillator and the Tent and Logistic maps. Numerical results indicate that the permutation entropy can in principle be used to detemine the entropy rate of a system, and thu...

In a previous paper (Comput. Methods Appl. Mech. Engrg 170, 223-237, 1999) we introduced a new method for computing the dominant Lyapunov exponent of a chaotic map by using spatial integration involving a matrix norm. We conjectured that this sequence of integrals decayed proportional to 1/n. We now prove this conjecture and derive a bound on the next term in the asymptotic expansion of the ter...

Synchronization properties of two identical mutually coupled Duffing oscillators with parametric modulation in one of them are studied. Intermittent lag synchronization is observed in the vicinity of saddle-node bifurcations where the system changes its dynamical state. This phenomenon is seen as intermittent jumps from phase to lag synchronization, during which the chaotic trajectory visits cl...

Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical dissipative chaotic Duffing oscillator. The similarities and differences from the classical oscillator are examined; in particular, a new concept of quantum maps is introduced, and alterations in the classical strange attractor due to the presence of scale-dependent quantu...

Predicting extrema of chaotic systems in high-dimensional phase space remains a challenge. Methods, which give extrema that are valid in the long term, have thus far been restricted to models of only a few variables. Here, a method is presented which treats extrema of chaotic systems as belonging to discretised manifolds of low dimension (low-D) embedded in high-dimensional (high-D) phase space...

A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and grad...

n this article we first show a theory that a Wiener-type cascade I dynamical model, in which a simple linear plant is used as the dynamic subsystem and a three-layer feed-forward artificial neural network is employed as the nonlinear static subsystem, can uniformly approximate a continuous trajectory of a general nonlinear dynamical system with arbitrarily high precision on a compact time domai...

Abstract In this paper, evolutionary algorithms are proposed to compute the optimal parameters of Gaussian Radial Basis Adaptive Backstepping Control (GRBABC) for chaotic systems. Generally, parameters are chosen arbitrarily, so in several cases this choice can be tedious. Also, stability cannot be achieved when the parameters are inappropriately chosen. The optimal design problems are to intro...