Effect of kernels on spatio-temporal patterns of a non-local prey-predator model

Pal, Swadesh; Ghorai, S.; Banerjee, Malay

doi:10.1016/j.mbs.2019.01.011

Cited by 17 publications

(10 citation statements)

References 26 publications

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“…These different types of kernel functions include top-hat kernel, Gaussian kernel, Laplacian kernel, triangular kernel, parabolic kernel, etc. [40][41][42]. Among these kernel functions, the simplest one is the symmetric top-hat kernel which is basically a step function, and incorporation of it in the modeling approach can lead to very rich and complex spatiotemporal pattern formations [40,42].…”

Section: Introductionmentioning

confidence: 99%

“…They further showed that the incorporation of nonlocal interactions in the classical Rosenzweig-MacArthur model can produce Turing patterns, while the local counterpart of it is unable to do so [47]. Some other interesting works on the impacts of nonlocal interactions on spatiotemporal dynamics for two-species models can be found in [40,[48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

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

2020

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2020

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“…In this study, we have used the top-hat kernel to model the nonlocal intra-specific interactions as a starting point. It would be interesting to validate our observations with other forms of kernel, namely parabolic, triangular, Laplacian and Gaussian kernels (Merchant and Nagata 2011;Pal et al 2019;Segal et al 2013), as the nature of nonlocal interaction varies from one species to another. Nevertheless, nonlocality could arise for the inter-specific competitions (Banerjee and Volpert 2016).…”

Section: Discussionmentioning

confidence: 80%

“…The nonlocal competitions are incorporated in the modeling approach through convolution integrals with a specific kernel function and hence, a system of integro-differential equations arise (Autry et al 2018;Banerjee and Volpert 2016;Britton 1989;Tanzy et al 2013). Examples of kernel function include top-hat, triangular, parabolic, Gaussian and Laplacian kernels (Manna et al 2020;Merchant and Nagata 2011;Pal et al 2019;Segal et al 2013).…”

Section: Introductionmentioning

confidence: 99%

“…A considerable number of studies on prey-predator systems with spatial kernels to model nonlocal interaction have been conducted over the last decade and some interesting works can be found in Autry et al (2018), Banerjee and Volpert (2016), Bayliss and Volpert (2017), Manna et al (2020), Merchant and Nagata (2011), Merchant and Nagata (2015), Pal et al (2018), Pal et al (2019). However, a very limited number of works on nonlocal competition models can be found in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Pattern Formation in a Three-Species Cyclic Competition Model

2021

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In nature, different species compete among themselves for common resources and favorable habitat. Therefore, it becomes really important to determine the key factors in maintaining the bio-diversity. Also, some competing species follow cyclic competition in real world where the competitive dominance is characterized by a cyclic ordering. In this paper, we study the formation of a wide variety of spatiotemporal patterns including stationary, periodic, quasi-periodic and chaotic population distributions for a diffusive Lotka-Volterra type three-species cyclic competition model with two different types of cyclic ordering. For both types of cyclic ordering, the temporal dynamics of the corresponding non-spatial system show the extinction of two species through global bifurcations such as homoclinic and heteroclinic bifurcations. For the spatial system, we show that the existence of Turing patterns is possible for a particular cyclic ordering, while it is not the case for the other cyclic ordering through both the analytical and numerical methods. Further, we illustrate an interesting scenario of short-range invasion as opposed to the usual invasion phenomenon over the entire habitat. Also, our study reveals that both the stationary and dynamic population distributions can coexist in different parts of a habitat. Finally, we extend the spatial system by incorporating nonlocal intra-specific competition terms for all the three competing species. Our study shows that the introduction of nonlocality in intra-specific competitions stabilizes the system dynamics by transforming a dynamic population distribution to stationary. Surprisingly, this nonlocality-induced stationary pattern formation leads to the extinction of one species and hence, gives rise to the loss of bio-diversity for intermediate ranges of nonlocality. However, the bio-diversity can be restored for sufficiently large extent of nonlocality.

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Spatio-temporal dynamics of an SIS model with nonlinear incidence and nonlocal disease transmission

2023

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Effect of kernels on spatio-temporal patterns of a non-local prey-predator model

Cited by 17 publications

References 26 publications

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

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

Pattern Formation in a Three-Species Cyclic Competition Model

Spatio-temporal dynamics of an SIS model with nonlinear incidence and nonlocal disease transmission

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