Modelling and Simulation of some Bifurcations of Nonlinear Systems with Additive Noise

H.G. Davies (Canada)


nonlinear systems, bifurcations, control, noise, simulation, stability


Modelling of nonlinear dynamical systems very often involves numerical simulation. Two nonlinear systems are examined with bifurcations of the response from one form to another as a control parameter is swept slowly through the bifurcation. For one of the systems, low-level noise can have a significant influence on the response, even the computer noise inherent in any numerical simulation, so that care must be taken in simulating such systems. An asymptotic analysis is given that explains the effects of (i) stabilisation of one form of the response by sinusoidal variation of a control parameter, but (ii) destabilization by increasing noise level. Control charts are obtained of parameter values that quench the bifurcation, and so provide a way to control the response.

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