Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems

Fasani, Stefano; Rinaldi, Sergio

doi:10.1016/j.ecolmodel.2011.07.002

Cited by 27 publications

(17 citation statements)

References 17 publications

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“…Most of the time one can find stationary spot pattern (hot spot or cold spot) as a resulting pattern for parameters within the Turing domain (Alonso et al, 2002;Banerjee, 2010;Fasani and Rinaldi, 2011;Sun et al, 2009;Wang et al, 2007;Volpert and Petrovskii, 2009). It is interesting to note that the instability of steady-state for temporal models of predator-prey interaction leads to either oscillatory coexistence state or extinction of one or both the species.…”

Section: Introductionmentioning

confidence: 98%

Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model

Banerjee

Abbas

2015

Ecological Complexity

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Section: Introductionmentioning

confidence: 98%

Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model

Banerjee

Abbas

2015

Ecological Complexity

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“…However, early models had to assume prey Allee effects and predator selfinhibition to meet this assumption (Alonso et al 2002;Fasani and Rinaldi 2011). In fact, many mechanisms that allow spatially inhomogeneous dynamics also result in the predator acting as an activator and the prey acting as an inhibitor.…”

Section: Introductionmentioning

confidence: 99%

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Pedersen

Marleau

Granados

et al. 2016

The American Naturalist

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Community interactions (e.g., predation, competition) can be characterized by two factors: their strengths and how they are structured between and within species. Both factors play a role in determining community dynamics. In addition to trophic interactions, dispersal acts as an interaction between separate populations. As with other interactions, the structure of dispersal can affect the stability of a system. However, the primary structure that has been studied in consumer-resource models has been hierarchical dispersal, where between-patch dispersal rates increase with trophic level. Here we use analytical, numerical, and simulation approaches on a two-patch, three-species metacommunity model to investigate the relationship between structure and community stability and resilience. We show that metacommunity stability is greater in systems with both weak and strong dispersal rates. Our system is stabilized by the formation of patterns when predators disperse frequently and herbivores disperse rarely, and via asynchrony when both predators and herbivores disperse infrequently. Our results show how interaction strengths within both trophic and spatial networks shape metacommunity stability.

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“…It is important to note that Γ(k, M) < 0 and ∆(k, M) > 0 as M → 0+ if we assume that (u * , v * ) is locally asymptotically stable for the temporal model (10)- (11). One can easily verify that lim M→0+ Γ(k, M) = a 11 and lim M→0+ ∆(k, M) = −a 12 a 21 .…”

Section: Spatial Hopf Bifurcationmentioning

confidence: 99%

“…Luckinbill [9,10] has also studied the effect of dispersal on stability as well as persistence/extinction of population over a longer period of time. Based on these data, works are done where the prey-predator models with spatial distribution are considered for various ecological processes [11], such as plankton patchiness [12][13][14], semiarid vegetation patterns [15], invasion by exotic species [16,17] etc. (see also [18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey

2018

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Spatiotemporal pattern formation in integro-differential equation models of interacting populations is an active area of research, which has emerged through the introduction of nonlocal intra-and inter-specific interactions. Stationary patterns are reported for nonlocal interactions in prey and predator populations for models with prey-dependent functional response, specialist predator and linear intrinsic death rate for predator species. The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators. We derive the conditions of the Turing and of the spatial Hopf bifurcation around the coexisting homogeneous steady-state and verify the analytical results through extensive numerical simulations. Bifurcations of spatial patterns are also explored numerically.

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Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems

Cited by 27 publications

References 17 publications

Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model

Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model

Nonhierarchical Dispersal Promotes Stability and Resilience in a Tritrophic Metacommunity

Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey

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