A liénard oscillator resonant tunnelling diode-laser diode hybrid integrated circuit: model and experiment

We report on a hybrid optoelectronic integrated circuit based on a resonant tunnelling diode driving an optical communications laser diode. This circuit can act as a voltage controlled oscillator with optical and electrical outputs. We show that the oscillator operation can be described by Liénard's equation, a second order nonlinear differential equation, which is a generalization of the Van der Pol equation. This treatment gives considerable insight into the potential of a monolithic version of the circuit for optical communication functions including clock recovery and chaotic source applications

Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in Physics Please Lakshmanan for figures (e-mail: [email protected]

Construction of classes of circuit-independent chaotic oscillatorsusing passive-only nonlinear devices

Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and the evolution of the two-dimensional sinusoidal oscillator dynamics into a higher dimensional state space is clearly recognized. We further discuss three architectures into which autonomous chaotic oscillators can be decomposed. Based on one of these architectures we classify a large number of the available chaotic oscillators and propose a novel reconstruction of the classical Chua’s circuit. The well-known Lorenz system of equations is also studied and a simplified model with equivalent dynamics, but containing no multipliers, is introduced

Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices

Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and the evolution of the two-dimensional sinusoidal oscillator dynamics into a higher dimensional state space is clearly recognized. We further discuss three architectures into which autonomous chaotic oscillators can be decomposed. Based on one of these architectures we classify a large number of the available chaotic oscillators and propose a novel reconstruction of the classical Chua's circuit. The well-known Lorenz system of equations is also studied and a simplified model with equivalent dynamics, but containing no multipliers, is introduce

Conservative Chaos Generators with CCII+ Based on Mathematical Model of Nonlinear Oscillator

In this detailed paper, several novel oscillator\'s configurations which consist only of five positive second generation current conveyors (CCII+) are presented and experimentally verified. Each network is able to generate the conservative chaotic attractors with the certain degree of the structural stability. It represents a class of the autonomous deterministic dynamical systems with two-segment piecewise linear (PWL) vector fields suitable also for the theoretical analysis. Route to chaos can be traced and observed by a simple change of the external dc voltage. Advantages and other possible improvements are briefly discussed in the text

Nonlinear Resistor with Polynomial AV Characteristics and Its Application in Chaotic Oscillator

This paper shows the realization of two terminal devices with an arbitrary polynomial nonlinearity up to the fifth order. The proposed design procedure is completely systematic using minimum of components. The very heart of our conception is four-channel four-quadrant analog multiplier MLT04. The implementation of synthesized nonlinear resistor as a general nonlinearity in chaotic oscillator is also presented and experimentally verified