On bifurcations in a chaotically stirred excitable medium
The authors study a systematic numerical and theoretical analysis of the bifurcation scenario of chaotically stirred excitable media. They find supercritical and subcritical Hopf bifurcation and a hysteresis loop beside the well-known saddle-node bifurcations associated with propagation failure of excitable media. The bifurcations are described in terms of two parameters signifying the excitability of the reacting medium and the strengh of the chaotic stirring, respectively. The solution behaviour, in particular at the bifurcation points, is analytically described by means of a nonperturbative variational method. In Section 2 the stirred excitable medium is introduced. Section 3 provides a thorough numerical investigation of the bifurcation scenario of this model. In Section 4, the nonperturbative method is reviewed to be used to describe analytically the bifurcations and the solutions in terms of equation parameters. This is performed in Section 5, where the solutions are compared with those of numerical simulations of the full stirred excitable lamellar model.
scientific article; zbMATH DE number 5534905
scientific article