5,993 research outputs found
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
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