Hopf bifurcations in a fractional reaction–diffusion model for the invasion and development of tumor
AbstractThe phenomenon of hopf bifurcation has been well-studied and applied to
many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that more complex hopf bifurcation phenomena are possible when the complexity of the reaction and interaction increases. Results are discussed not only for fractional reaction
diffusion equations, but also for ordinary differential equations and standard reaction diffusion equations as well. As a matter of fact, we demonstrated that the reactiondiffusion system portray interesting hopf bifurcation as the complexity of the equation changes. Just to say, a single equation will show hopf bifurcation of lesser complexity than those of a system of equations. The target model is the fractional reaction
diffusion model for tumor invasion, conceived and analysed in situ. A uniform hopf bifurcation where the spatial and temporal sub critical and supercritical hopf bifurcations coincide is discussed for this model in a numerical simulation.