Investigations of the autowave solutions of a model of structured media with spatial and temporal nonlocality

A system of partial differential equations, describing nonlinear medium with spatial nonlocality is investigated. Invariant travelling wave solutions are studied in detail. Existence of period doubling cascade leading to the creation of a chaotic attractor is proved via the analysis of the Feigenbaum universality and the limit cycle multiplicators calculation. Internal bifurcations of chaotic attractor are studied. The influence of higher-derivative terms, corresponding to temporal nonlocality, on the soliton-like solutions appearance is investigated.