Spatiotemporal Patterns in Ecology and Epidemiology

Malchow, Horst; Petrovskii, Sergei; Venturino, Ezio

doi:10.1201/9781482286137

Cited by 178 publications

(186 citation statements)

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“…'r' and 's' denote intrinsic growth rates for prey and predator, respectively. 'K' is the environmental carrying capacity for prey population, 'c' is the per capita capturing rate of prey by a predator per unit time, and 'h' is proportionality constant that indicates the prey amount needed to feed a predator in equilibrium conditions [3,4].…”

Section: Introductionmentioning

confidence: 99%

Stochastic persistence and stability analysis of a modified Holling–Tanner model

Mandal

Banerjee

2012

Math Methods in App Sciences

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The article aims to study the basic dynamical features of a modified Holling–Tanner prey–predator model with ratio‐dependent functional response. We have proved the global existence of the solution for the deterministic model. The parametric restriction for persistence of both species is also obtained along with the proof of local asymptotic stability of the interior equilibrium point(s). Conditions for local bifurcations of interior equilibrium points are provided. The global dynamic behavior is examined thoroughly with supportive numerical simulation results. Next, we have formulated the stochastic model by perturbing the intrinsic growth rates of prey and predator populations with white noise terms. The existence uniqueness of solutions for stochastic model is established. Further, we have derived the parametric restrictions required for the persistence of the stochastic model. Finally, we have discussed the stochastic stability results in terms of the first and second order moments. Numerical simulation results are provided to support the analytical findings. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Stochastic persistence and stability analysis of a modified Holling–Tanner model

Mandal

Banerjee

2012

Math Methods in App Sciences

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“…The non-coherent response, which is induced by the localized short-time highintensity influence of noise, persists significantly longer in the case when the perturbation is applied to a high-sensitive region (with higher ILS) than in case of the influence to the region with low values of ILS. The obtained results indicate the non-homogeneity of the response of system (6) in the regime of partial coherence.…”

Section: Local Sensitivity To Noisementioning

confidence: 81%

Local sensitivity of spatiotemporal structures

et al. 2018

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We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the asymptotic scaling of local-in-space, finite-time Lyapunov Exponents. For a system of nonlocally-coupled Rössler oscillators, we show that deviations of this index reflect the sensitivity to noise and the onset of spatial chaos for the patterns where coherence and incoherence regions coexist.

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“…Lemma 8. Assume that ∈ C 2 , ([0, T ′ ] × R, R) with ∈ (0, 1) ∪ (1,2) and v 0 (x) ∈ C(R, R) in the above equation. Then, for every ∈ (0,…”

Section: Appendixmentioning

confidence: 99%

“…Predator-prey systems are basis models in modeling interspecific action, and there are many important results on the analysis and applications on kinetic systems. [1][2][3] Since the spatial distribution of individuals may also affect the persistence and other properties of individuals, the spatial-temporal models with predator-prey nonlinearities also attract much attentions (see some results by Cantrell and Cosner 4 and Du and Shi 5 ). In particular, propagation phenomena have been observed and investigated to characterize the spatial expansion of individuals.…”

Section: Introductionmentioning

confidence: 99%

Spatial invasion dynamics for a time period predator‐prey system

Lin

Wang

2018

Math Methods in App Sciences

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This paper is concerned with the propagation theory of a predator‐prey system in a periodic environment. We consider the invasion process that the prey is the aboriginal, whereas the predator is the invader. If the initial habitat size of the predator is finite, then the asymptotic speed of spreading of the predator is given. Furthermore, the existence and nonexistence of traveling wave solutions are obtained, which defined a minimal wave speed of traveling wave solutions. Our results imply that the minimal wave speed of traveling wave solutions is equal to the asymptotic speed of spreading of the predator.

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Spatiotemporal Patterns in Ecology and Epidemiology

Cited by 178 publications

References 0 publications

Stochastic persistence and stability analysis of a modified Holling–Tanner model

Stochastic persistence and stability analysis of a modified Holling–Tanner model

Local sensitivity of spatiotemporal structures

Spatial invasion dynamics for a time period predator‐prey system

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