Simple model for bifurcations ranging up to chaos in thermal lens oscillations and associated phenomena

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Abstract
A very simple model is designed to understand dynamical states and bifurcations ranging up to chaos in thermal lens oscillations and associated hot-wire experiments. The present system is governed by partial-derivative equations in the case of bulk liquid and also at a free surface which is a boundary of the liquid. It is reduced to a set of three nonlinear ordinary differential equations with two control parameters to be studied within the framework of the theory of nonlinear dynamical systems. The model may evolve to chaos in three domains of the parameter plane. Metric and dynamical properties (generalized dimensions and entropies, and associated singularity spectra) of a (presumably) strange chaotic attractor produced by the model are determined. The overall good and sometimes striking agreement between the model and previously reported experimental results shows that we have reached a fair understanding of the experimental phenomena, much better than what has been hitherto possible.