An Interdisciplinary Journal

2001, Volume 4, Number 4, pp.390-396

On the Autowave Solutions of Some Model of Structured Media Accounting for Effects of Spatio-temporal Nonlocality
S.I. Skurativskyy

Results of the investigations of the continual model describing long nonlinear waves propagation in media with internal structure are presented. The model takes into account relaxing effects as well as spatial nonlocality associated with structure and manifesting in the high-rate processes. Using the group theory reduction we extract from the initial system of PDE three dimensional dynamical system describing a set of travelling wave solutions. This set is shown to contain a great variety of non-monotonic regimes, that do not occur in the analogous models without non-locality. We state the conditions assuring the existence of periodic, quasiperiodic and soliton-like solutions. Their further evolution is investigated by means of numerical simulation, enabling to extract fine characteristics of multiperiodic and chaotic regimes, corresponding to certain domains of parameter space, to trace various scenarios of chaotization and bifurcations of strange attractors
Key words: "internal" variable, limit cycle, chaotic attractor, homoclinic trajectory

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