In this contribution we report on a transition to high-dimensional chaos through three-frequency quasiperiodic behavior. The resulting chaotic attractor has a one positive and two null Lyapunov exponents. The transition occurs at the point at which two symmetry related threedimensional tori merge in a crisis-like bifurcation. The route can be summarized as: 2D torus → 3D torus→ high-dimensional...

A new chaotic system is presented using a single parameter for a two-scroll attractor with high complexity, high chaoticity and widely chaotic range. The system employs two quadratic nonlinearities and two piecewiselinear nonlinearities. The high chaoticity is measured by the the maximum Lyapunov Exponent of 0.429 and the high complexity is measured by the Kaplan-Yorke dimension of 2.3004. Dyna...

It has been widely experienced that tracking (targeting) a periodic orbit embedded within a chaotic attractor often encounters an essential issue of numerical sensitivity. In this paper, we develop an effective digital tracker for continuous-time chaotic orbit tracking, which is insensitive to numerical errors. The design is based on some advanced digital redesign techniques equipped with a pre...

Recently, a novel three-dimensional highly chaotic attractor has been discovered by Srisuchinwong and Munmuangsaen (2010). This paper investigates the adaptive control and synchronization of this highly chaotic attractor with unknown parameters. First, adaptive control laws are designed to stabilize the highly chaotic system to its unstable equilibrium point at the origin based on the adaptive ...

Recent work has considered the possibility of utilizing symbolic representations of controlled chaotic orbits for communicating with chaotically behaving signal generators. The success of this type of nonlinear digital communication scheme relies on partitioning the phase space properly so that a good symbolic dynamics can be defined. A central problem is then how to encode an arbitrary message...

Invariant sets embedded in a chaotic attractor can generate time averages that diier from the average generated by typical orbits on the attractor. Motivated by two diierent topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We presen...

Keywords: System of ordinary quadratic differential equations Linear transformations Boundedness Limit cycle Chaotic attractor Saddle focus Ricker discrete population model a b s t r a c t The wide class of 3-D autonomous systems of quadratic differential equations, in each of which either there is a couple of coexisting limit cycles or there is a couple of coexisting chaotic attractors, is fou...

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windo...

When a dynamical system possesses certain symmetry, there can be an invariant subspace in the phase space. In the invariant subspace there can be a chaotic attractor. As a parameter changes through a critical value, the chaotic attractor can lose stability with respect to perturbations transverse to the invariant subspace. We show that the loss of the transverse stability can lead to a symmetry...

This paper investigates the approach for revealing pathological speech signal based on estimating specific geometric structure of Lorenz attractor in a chaotic regime. Analysis of the Lorenz attractor on the basis of proposed nonlinear decomposition into matrix series is developed. This analysis permits to estimate the values of characteristic parameters (including control one) of Lorenz attrac...