Mathematical modeling of traveling autosolitons in fractional-order activator-inhibitor systems

摘要

In the article,basic properties of traveling spatially nonhomogeneous auto-wave solutions in nonlinear fractional-order reaction-diffusion systems are investigated.Such solutions,called autosolitons,arise in a stability region of the system and can coexist with the spatially homogeneous states.By a linear stability analysis and computer simulation,it is shown that the order of the fractional derivative can substantially change the properties of such auto-wave solutions and significantly enrich nonlinear system dynamics.The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol-FitzHugh-Nagumo model.A common picture of traveling auto-waves including series in time-fractional two-component activator-inhibitor systems is presented.The results obtained in the article for the distributed system have also been of interest for nonlinear dynamical systems described by fractional ordinary differential equations.