Formation of regular spatial patterns in ratio-dependent predator-prey model driven by spatial colored-noise

Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of spatial noise for this system when the parameters are in the Turing space, above which the regular spatial patterns appear in two dimensions, but under which there are not regular spatial patterns produced. In particular, we investigate in two-dimensional space the formation of regular spatial patterns with the spatial noise added in the side and the center of the simulation domain, respectively.Comment: 4 pages and 3 figure

Spatiotemporal complexity of a ratio-dependent predator-prey system

In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.Comment: 6pages, revtex

Community-driven dispersal in an individual-based predator-prey model

We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness measure. Dispersal of individuals to nearby communities occurs whenever their fitness falls below a predefined tolerance threshold. The spatiotemporal dynamics of the model is described in terms of this threshold. We compare this dynamics with the one obtained through density-independent dispersal and find marked differences. In the community-driven scenario, the spatial correlations in the population density do not vary in a linear fashion as we increase the tolerance threshold. Instead we find the system to cross different dynamical regimes as the threshold is raised. Spatial patterns evolve from disordered, to scale-free complex patterns, to finally becoming well-organized domains. This model therefore predicts that natural populations, the dispersal strategies of which are likely to be influenced by their local environment, might be subject to complex spatiotemporal dynamics.Comment: 43 pages, 7 figures, vocabulary modifications, discussion expanded, references added, Ecological Complexity accepte

Phase Transitions and Oscillations in a Lattice Prey-Predator Model

A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated by dynamical mean-field approximations and extensive numerical simulations. It is shown that the stationary state phase diagram is divided into two phases: a pure prey phase and a coexistence phase of preys and predators in which temporal and spatial oscillations can be present. The different type of phase transitions occuring at the boundary of the prey absorbing phase, as well as the crossover phenomena occuring between the oscillatory and non-oscillatory domains of the coexistence phase are studied. The importance of finite size effects are discussed and scaling relations between different quantities are established. Finally, physical arguments, based on the spatial structure of the model, are given to explain the underlying mechanism leading to oscillations.Comment: 11 pages, 13 figure