Pattern Formation in a Prey-Predator Model with Nonlocal Interaction Terms

2016 ◽  
pp. 27-39 ◽  
Author(s):  
Malay Banerjee ◽  
Moitri Sen ◽  
Vitaly Volpert
Keyword(s):  
Pattern Formation ◽  
Nonlocal Interaction ◽  
Interaction Terms ◽  
Predator Model

scholarly journals Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 101 ◽  
Author(s):  
Kalyan Manna ◽  
Vitaly Volpert ◽  
Malay Banerjee
Keyword(s):  
Prey Species ◽  
Population Distribution ◽  
Chaotic Oscillation ◽  
Turing Instability ◽  
Transient Dynamics ◽  
Nonlocal Interaction ◽  
Interaction Terms ◽  
Population Distributions ◽  
Predator Model ◽  
Spatiotemporal Models

Investigation of interacting populations is an active area of research, and various modeling approaches have been adopted to describe their dynamics. Mathematical models of such interactions using differential equations are capable to mimic the stationary and oscillating (regular or irregular) population distributions. Recently, some researchers have paid their attention to explain the consequences of transient dynamics of population density (especially the long transients) and able to capture such behaviors with simple models. Existence of multiple stationary patches and settlement to a stable distribution after a long quasi-stable transient dynamics can be explained by spatiotemporal models with nonlocal interaction terms. However, the studies of such interesting phenomena for three interacting species are not abundant in literature. Motivated by these facts here we have considered a three species prey–predator model where the predator is generalist in nature as it survives on two prey species. Nonlocalities are introduced in the intra-specific competition terms for the two prey species in order to model the accessibility of nearby resources. Using linear analysis, we have derived the Turing instability conditions for both the spatiotemporal models with and without nonlocal interactions. Validation of such conditions indicates the possibility of existence of stationary spatially heterogeneous distributions for all the three species. Existence of long transient dynamics has been presented under certain parametric domain. Exhaustive numerical simulations reveal various scenarios of stabilization of population distribution due to the presence of nonlocal intra-specific competition for the two prey species. Chaotic oscillation exhibited by the temporal model is significantly suppressed when the populations are allowed to move over their habitat and prey species can access the nearby resources.

Nonlocal interaction driven pattern formation in a prey–predator model

2017 ◽  
Vol 308 ◽  
pp. 73-83 ◽  
Author(s):  
Canrong Tian ◽  
Zhi Ling ◽  
Lai Zhang
Keyword(s):  
Pattern Formation ◽  
Nonlocal Interaction ◽  
Predator Model

Pattern Formation in a Two-dimensional Space Diffusive Prey-predator Model

2012 ◽  
Vol 12 (19) ◽  
pp. 2016-2025
Author(s):  
Mohd Hafiz Mohd ◽  
Yahya Abu Hasan
Keyword(s):  
Pattern Formation ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Predator Model

scholarly journals Pattern formation of a nonlocal, anisotropic interaction model

2018 ◽  
Vol 28 (03) ◽  
pp. 409-451 ◽  
Author(s):  
Martin Burger ◽  
Bertram Düring ◽  
Lisa Maria Kreusser ◽  
Peter A. Markowich ◽  
Carola-Bibiane Schönlieb
Keyword(s):  
Pattern Formation ◽  
Tensor Field ◽  
Mean Field ◽  
Interaction Model ◽  
Gradient Flow ◽  
Two Dimensions ◽  
Nonlocal Interaction ◽  
Anisotropic Model ◽  
Interaction Forces ◽  
Interacting Particle

We consider a class of interacting particle models with anisotropic, repulsive–attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called Kücken–Champod model describing the formation of fingerprint patterns. This class of models can be regarded as a generalization of a gradient flow of a nonlocal interaction potential which has a local repulsion and a long-range attraction structure. In contrast to isotropic interaction models the anisotropic forces in our class of models cannot be derived from a potential. The underlying tensor field introduces an anisotropy leading to complex patterns which do not occur in isotropic models. This anisotropy is characterized by one parameter in the model. We study the variation of this parameter, describing the transition between the isotropic and the anisotropic model, analytically and numerically. We analyze the equilibria of the corresponding mean-field partial differential equation and investigate pattern formation numerically in two dimensions by studying the dependence of the parameters in the model on the resulting patterns.

scholarly journals Pattern formation in a diffusive intraguild predation model with nonlocal interaction effects

AIP Advances ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 035046 ◽  
Author(s):  
Renji Han ◽  
Binxiang Dai ◽  
Yuming Chen
Keyword(s):  
Pattern Formation ◽  
Intraguild Predation ◽  
Interaction Effects ◽  
Nonlocal Interaction

Effects of boundary conditions on pattern formation in a nonlocal prey–predator model

2020 ◽  
Vol 79 ◽  
pp. 809-823 ◽  
Author(s):  
Swadesh Pal ◽  
Malay Banerjee ◽  
S. Ghorai
Keyword(s):  
Pattern Formation ◽  
Boundary Conditions ◽  
Predator Model
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