Objective
It is proposed to carry out an interdisciplinary research project to analyse the effect of noise on the dynamics of multistable chaotic systems, and to tackle the problem of control in such systems. The results of the fundamental research will be applied to the analysis of the dynamics of nonlinear optical devices and of cardiovascular flow.
The research programme is motivated by the fact that almost all systems, whether in nature or in technology, are noisy and nonlinear. Frequently, they are characterised by two or more coexisting attractors that can often be chaotic. Analysis of the stochastic dynamics, and the development of methods for controlling such systems, are long-standing and challenging problems. They are of broad interdisciplinary interest from the point of view of fundamental research, and of great importance in view of a host of practical applications.
The remarkable progress achieved recently in the fields of chaos control, synchronisation and fluctuational non-equilibrium dynamics - in which the co-applicants have played not insignificant roles - provides the necessary basis for the proposed research. In the course of earlier collaborative investigations, the complementary expertise of some of the participants has already been shown to provide a potent combination for the solution of problems in chaotic and stochastic dynamics.
It is now envisaged that joint efforts, involving specialists in fundamental and applied physics, will lead to a substantial breakthrough in the understanding and control stochastic dynamics in multistable chaotic systems. It is anticipated in particular that the investigation of the statistical properties of fluctuational trajectories in chaotic systems and maps, and in the analysis of synchronisation, will reveal optimal paths underlying the processes of noise induced escape and inter-well transitions. Their existence will allow one to consider stochastic dynamics in such systems in general terms using the methods of nonlinear dynamics. A knowledge of the optimal paths and corresponding optimal forces will provide a solution of the energy-optimal switching problem in chaotic multistable systems, and thus pave the way to the design of new methods of chaos control.
The understanding of stochastic dynamics in multistable chaotic systems thereby gained will then be applied immediately to analyse stochastic dynamics in semiconductor lasers and in cardiovascular flow. The fundamental part of the proposed research will be focused initially on the detailed investigation of stochastic dynamics in continuous chaotic systems with non-hyperbolic (CR4, CO, CR5, CR6) and quasi-hyperbolic (CR5, CO, CR4, CR6) attractors, and weakly dissipative systems with homoclinic tangles (CR8, CR1, CR6, CR3). The research will be then extended to the analysis of the stochastic dynamics in chaotic maps (CR3, CR4, CR5, CO). Another important extension is related to an analysis of the effect of noise on synchronisation in a system of coupled oscillators (CR7, CR5, CO, CR4). Attempts will also be made to extend the technique to analyse the spatio-temporal dynamics of an ensemble of coupled FitzHugh - Nagumo systems (CR7, CR6, CR4). The results of the fundamental research will be applied to the analysis of the stochastic dynamics in semiconductor laser with modulated current or delayed feedback (CR2, CR4, CR5). The latter will open the way to analysis of the whole new class of systems described by the delayed differential equations. The key ingredient here is a new technique (CR2) of constructing a series of finite dimensional analytical maps.
Finally, the topical and challenging problem of modelling cardiovascular dynamics will be considered (CR9, CR5, CO, CR4, CR7). The research will be based on the recent suggestion that the circulatory system can usefully be modelled (CR9) as a system of five coupled, autonomous, nonlinear oscillators. The results of the modelling will be compared with the results of physiological experiments (CR9, CO).
Call for proposal
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LA1 4YB Lancaster
United Kingdom