Asymptotic Behaviour of Nonlinear Systems

Asymptotic Behaviour of Nonlinear Systems

Stability and Asymptotic Behaviour of Nonlinear Systems: an Introduction

To motivate a study of asymptotic behaviour of nonlinear systems modelled by ordinary differential equations and differential inclusions, we indicate how such equations/inclusions arise naturally in control of dynamical process by feedback. The concept of control pertains to modifying the behaviour of the process, by manipulation of inputs to the process, in order to achieve some prescribed goa...

Asymptotic Behaviour of Platoon Systems

In this paper we study the asymptotic behaviour of various platoon-type systems using the general theory developed by the authors in a recent article. The aim is to steer an infinite number of vehicles towards a target configuration in which each vehicle has a prescribed separation from its neighbour and all vehicles are moving at a given velocity. More specifically, we study systems in which s...

Asymptotic behaviour of graded components of local cohomology modules

This article has no abstract.

Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems

In this paper, we consider a three-parameter class of Liénard type nonlinear dissipative systems of the form ẍ + (b+ 3kx)ẋ + k2x3 + bkx2 + λx = 0. Since such dissipative systems admit an eight-parameter Lie group of point transformations, it follows that there exists a (complex) point transformation mapping such a system into the free particle system ẍ = 0. Normally, such an explicit point tran...