Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 34, Issue 5, Pages 1614-1636Publisher
WILEY
DOI: 10.1002/num.22205
Keywords
coexistence; exponential time differencing method; fractional Fourier transform; global and local stability; nonlinear; predator-prey model; reaction-diffusion system
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In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species systems. We analyze the linear stability of stationary solutions in the one-dimensional multisystem modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three-interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyses to determine the global dynamics of the system. In the presence of a fractional diffusion term, we introduced a fractional Fourier transform for solving the system modeled by fractional partial differential equations. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator with exponential accuracy and a completely straightforward extension to high spatial dimensions. The scheme is described in detail and justified by a number of computational experiments.
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