Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponent System (Advances in Applied Mathematics and Mechanics, 2021)
In this work, we examine the mathematical analysis and numerical simulationof pattern formation in a subdiffusive multicomponent fractional-reaction-diffusionsystem that models the spatial interrelationship between two preys andpredator species. The major result is centered on the analysis of the system for linearstability. Analysis of the main model reflects that the dynamical system is locallyand globally asymptotically stable. We propose some useful theorems based on theexistence and permanence of the species to validate our theoretical findings. Reliableand efficient methods in space and time are formulated to handle any space fractionalreaction-diffusion system. We numerically present the complexity of the dynamics thatare theoretically discussed. The simulation results in one, two and three dimensionsshow some amazing scenarios.