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Spatiotemporal complexity of a ratio-dependent predator-prey system.
The study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves, which may help to better understand the dynamics of an aquatic community in a real marine environment. Expand
Pattern formation of a predator-prey system with Ivlev-type functional response
This paper investigates the spatial pattern formation of a predator–prey system with prey-dependent functional response Ivlev-type and reaction-diffusion and finds that with special initial conditions the system can emerge not only spiral pattern but also target pattern and so on, and the effect of these special conditions on the formation of spatial patterns is less and less with more and more iterations but the effect does not decay forever. Expand
An algorithm for solving the high-order nonlinear Volterra-Fredholm integro-differential equation with mechanization
  • Weiming Wang
  • Mathematics, Computer Science
  • Appl. Math. Comput.
  • 2006
The results indicated that the procedure voltfredproc of Taylor polynomial method is simple and effective, and could provide an accuracy approximate solution or exact solution of the high-order nonlinear Volterra–Fredholm integro-differential equation. Expand
The dynamical complexity of a Ivlev-type prey–predator system with impulsive effect ☆
Abstract Based on the classical predator–prey system with Ivlev-type functional response, an impulsive differential equations to model the process of periodic perturbations on the predator atExpand
Mechanization for solving SPP by reducing order method
In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of reduction of order approximation method for solving singular perturbationExpand
Spatiotemporal dynamics of a reaction?diffusion epidemic model with nonlinear incidence rate
In this paper, we investigate the complex dynamics of a reaction–diffusion I–R model with a nonlinear rate of incidence of saturated mass action under zero-flux boundary conditions. We give anExpand
A stochastic SIRS epidemic model with infectious force under intervention strategies
Abstract In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE)Expand
A stochastic SIRS epidemic model with nonlinear incidence rate
Investigation of the global dynamics of a general SIRS epidemic model with a ratio-dependent incidence rate and its corresponding stochastic differential equation version finds that random fluctuations introduced in the model can suppress disease outbreak, which can provide some useful control strategies to regulate disease dynamics. Expand
Complex patterns in a predator-prey model with self and cross-diffusion
In this paper, we present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self as well asExpand
Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge
Abstract In this paper, we investigate the spatiotemporal dynamics of a two-dimensional predator–prey model, which is based on a modified version of the Leslie–Gower scheme incorporating a preyExpand