Tetsushi Ueta

Yet another chaotic attractor

This Letter reports the finding of a new chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.

BIFURCATION ANALYSIS OF CHEN'S EQUATION

Anticontrol of chaos by making a nonchaotic system chaotic has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chens equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chens equation, thereby revealing its different features from some other chaotic models such as its origin, the Lorenz system.

Chaos in Circuits and Systems

Chaos in non-linear circuits: design methodology for autonomous chaotic oscillators, A.S. Elwakil and M.P. Kennedy chaotic wandering in simple coupled chaotic circuits, Y. Nishio intermittent chaos in phase-locked loops, T. Endo et al stochastic analysis of electrical circuits, M.A. van Wyk and J. Ding. Chaos in non-linear systems: chaos in neural networks - chaotic neuro-computer, Y. Horio and K. Aihara complex dynamical behaviour in nearly symmetric standard cellular neural networks, M. Forti and A. Tesi chaos in power electronics - use of chaotic switching for harmonic power redistribution in power converters, H.S.H. Chung et al experimental techniques for investigating chaos in electronics, C.K. Tse chaos in control systems - controller synthesis for periodically forced chaotic systems, M. Basso et al mechanism for taming chaos by weak harmonic perturbations, N. Inaba chaos in communication systems - using non-linear dynamics and chaos to solve signal processing tasks, M.J. Ogorzalek identification of a parametrized family of chaotic dynamics from time series, I. Tokuda and R. Tokunaga image processing in tunnelling phase logic cellular non-linear networks, T. Yang et al chaos in numerical computations - numerical approaches to bifurcation analysis, T. Ueta and H. Kawakami chaos in one-dimensional maps, M.A. van Wyk and W.-H. Steeb. (Part contents.)

On impulsive control of a periodically forced chaotic pendulum system

We consider impulsive control of a periodically forced pendulum system which has rich chaos and bifurcation phenomena. A new impulsive control method for chaos suppression of this pendulum system is developed. Some simple sufficient conditions for driving the chaotic state to its zero equilibrium are presented, and some criteria for eventually, exponentially asymptotical stability are established. This work provides a rigorous theoretical analysis to support some early experimental observations on controlling chaos in the periodically forced pendulum system.

Bifurcation of switched nonlinear dynamical systems

This paper proposes a method to trace bifurcation sets for a piecewise-defined differential equation. In this system, the trajectory is continuous, but it is not differentiable at break points of the characteristics. We define the Poincare mapping by suitable local sections and local mappings, and thereby it is possible to calculate bifurcation parameter values. As an illustrated example, we analyze the behavior of a two-dimensional nonlinear autonomous system whose state space is constrained on two half planes concerned with state dependent switching characteristics. From investigation of bifurcation diagrams, we conclude that the tangent and global bifurcations play an important role for generating various periodic solutions and chaos. Some theoretical results are confirmed by laboratory experiments.

BIFURCATIONS IN TWO-DIMENSIONAL HINDMARSH–ROSE TYPE MODEL

We analyze a two-dimensional Hindmarsh–Rose type model exhibiting properties of both Class 1 and Class 2 neurons. Although the system is two-dimensional and contains only four parameters, the obtained bifurcation diagrams show that the bifurcation structure satisfies conditions for emergence of both features with constant stimuli.

BIFURCATION AND CHAOS IN COUPLED BVP OSCILLATORS

Bonhoffer–van der Pol(BVP) oscillator is a classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region, create the double scroll attractor due to the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in the experimental laboratory.

BIFURCATION ANALYSIS OF CURRENT COUPLED BVP OSCILLATORS

The Bonhoffer-van der Pol (BVP) oscillator is a simple circuit implementation describing neuronal dynamics. Lately the diffusive coupling structure of neurons attracts much attention since the existence of the gap-junctional coupling has been confirmed in the brain. Such coupling is easily realized by linear resistors for the circuit implementation, however, there are not enough investigations about diffusively coupled BVP oscillators, even a couple of BVP oscillators. We have considered several types of coupling structure between two BVP oscillators, and discussed their dynamical behavior in preceding works. In this paper, we treat a simple structure called current coupling and study their dynamical properties by the bifurcation theory. We investigate various bifurcation phenomena by computing some bifurcation diagrams in two cases, symmetrically and asymmetrically coupled systems. In symmetrically coupled systems, although all internal elements of two oscillators are the same, we obtain in-phase, anti-phase solution and some chaotic attractors. Moreover, we show that two quasi-periodic solutions are disappeared simultaneously by the homoclinic bifurcation on the Poincare map and that a large quasi-periodic solution is generated by the coalescence of these quasi-periodic solutions, but it is disappeared by the heteroclinic bifurcation on the Poincare map. In the other case, we confirm the existence a conspicuous chaotic attractor in the laboratory experiments.

Bifurcation analysis of a piecewise smooth system with non‐linear characteristics

SUMMARY In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non-linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non-linear characteristics. Werst propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincare mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh-type oscillator containing a state- period-dependent switch. In the circuit, we cannd many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border-collision bifurcations. Some theoretical results are veried by laboratory experiments. Copyright ? 2005 John Wiley & Sons, Ltd.

Bifurcation in asymmetrically coupled BVP oscillators

BVP oscillator is the simplest mathematical model describing dynamical behavior of neural activity. Large scale neural network can often be described naturally by coupled systems of BVP oscillators. However, even if two BVP oscillators are merely coupled by a linear element, the whole system exhibits complicated behavior. In this letter, we analyze coupled BVP oscillators with asymmetrical coupling structure, besides, each oscillator has different internal resistance. The system shows a rich variety of bifurcation phenomena and strange attractors. We calculate bifurcation diagrams in two-parameter plane around which the chaotic attractors mainly appear and confirm relaxant phenomena in the laboratory experiments. We also briefly report a conspicuous strange attractor.