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Turing-Hopf bifurcation and spatio-temporal patterns of a ratio-dependent Holling-Tanner system with diffusion
- Publication Year :
- 2017
-
Abstract
- A diffusive ratio-dependent Holling-Tanner system subject to Neumann boundary conditions is considered. The existence of multiple bifurcations, including Turing-Hopf bifurcation, Turing-Truing bifurcation, Hopf-double-Turing bifurcation and triple-Turing bifurcation, are given. Among them, the Turing-Hopf bifurcation are carried out in details by the normal form method. We theoretically prove that the system exists various spatio-temporal patterns, such as, non-constant steady state, the spatially inhomogeneous periodic or quasi-periodic solution, etc. Numerical simulations are presented to illustrate our theoretical results.<br />Comment: 26 pages
- Subjects :
- Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1711.02787
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S0218127418501080