Analysis of a stochastic predator-prey system with mixed functional responses and Lévy jumps

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

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Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses

Complexity ◽

10.1155/2020/4285294 ◽

2020 ◽

Vol 2020 ◽

pp. 1-19

Author(s):

Kankan Sarkar ◽

Subhas Khajanchi ◽

Prakash Chandra Mali ◽

Juan J. Nieto

Keyword(s):

Growth Rate ◽

Hopf Bifurcation ◽

Dynamical Behavior ◽

Prey Population ◽

Uniform Persistence ◽

Functional Responses ◽

Normal Form Theory ◽

Predator Prey ◽

Center Manifold Theorem ◽

Prey System

In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.

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The Filippov Approach for Predator-Prey System Involving Mixed Type of Functional Responses

Differential Equations and Dynamical Systems ◽

10.1007/s12591-016-0322-x ◽

2016 ◽

Vol 28 (2) ◽

pp. 273-293

Author(s):

Komal Gupta ◽

Sunita Gakkhar

Keyword(s):

Mixed Type ◽

Functional Responses ◽

Predator Prey ◽

Prey System

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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

Complexity ◽

10.1155/2017/1950970 ◽

2017 ◽

Vol 2017 ◽

pp. 1-15 ◽

Cited By ~ 32

Author(s):

Guodong Liu ◽

Xiaohong Wang ◽

Xinzhu Meng ◽

Shujing Gao

Keyword(s):

Differential Equations ◽

Delay Differential Equations ◽

Time Delays ◽

Sufficient Conditions ◽

Predator Prey ◽

Persistence In Mean ◽

Predator Prey Model ◽

Prey System ◽

Delay Differential ◽

Lévy Jumps

In this paper, we explore an impulsive stochastic infected predator-prey system with Lévy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

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Space race functional responses

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2014.2121 ◽

2015 ◽

Vol 282 (1801) ◽

pp. 20142121 ◽

Cited By ~ 1

Author(s):

Henrik Sjödin ◽

Åke Brännström ◽

Göran Englund

Keyword(s):

Functional Response ◽

Community Dynamics ◽

Simple Structure ◽

Functional Responses ◽

Response Models ◽

Predator Prey ◽

Prey System ◽

Space Race ◽

Functional Response Models ◽

The Relationship

We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis–Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka–Volterra predator–prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.

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Predator-prey nutrient competition undermines predator coexistence

10.1101/535195 ◽

2019 ◽

Author(s):

Toni Klauschies ◽

Ursula Gaedke

Keyword(s):

Nutrient Limitation ◽

Uptake Rate ◽

Species Coexistence ◽

Logistic Growth ◽

Nutrient Competition ◽

Functional Responses ◽

Predator Prey ◽

Natural Systems ◽

Prey System ◽

Flow Through

AbstractContemporary theory of predator coexistence through relative non-linearity in their functional responses strongly relies on the Rosenzweig-MacArthur equations (1963) in which the (autotrophic) prey exhibits logistic growth in the absence of the predators. This implies that the prey is limited by a resource which availability is independent of the predators. This assumption does not hold under nutrient limitation where both prey and predators bind resources such as nitrogen or phosphorus in their biomass. Furthermore, the prey’s resource uptake-rate is assumed to be linear and the predator-prey system is considered to be closed. All these assumptions are unrealistic for many natural systems. Here, we show that predator coexistence on a single prey is strongly hampered when the prey and predators indirectly compete for the limiting resource in a flow-through system. In contrast, a non-linear resource uptake rate of the prey slightly promotes predator coexistence. Our study highlights that predator coexistence does not only depend on differences in the curvature of their functional responses but also on the type of resource constraining the growth of their prey. This has far-reaching consequences for the relative importance of fluctuation-dependent and -independent mechanisms of species coexistence in natural systems where autotrophs experience light or nutrient limitation.

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Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps

AIMS Mathematics ◽

10.3934/math.2022225 ◽

2021 ◽

Vol 7 (3) ◽

pp. 4068-4093

Author(s):

Yuanfu Shao ◽

Keyword(s):

Regime Switching ◽

Time Delays ◽

Optimal Harvesting ◽

Comparison Theory ◽

Predator Prey ◽

Prey System ◽

Persistence In The Mean ◽

Distributed Time Delays ◽

Stability In Distribution ◽

Lévy Jumps

<abstract><p>This work is concerned with a stochastic predator-prey system with S-type distributed time delays, regime switching and Lévy jumps. By use of the stochastic differential comparison theory and some inequality techniques, we study the extinction and persistence in the mean for each species, asymptotic stability in distribution and the optimal harvesting effort of the model. Then we present some simulation examples to illustrate the theoretical results and explore the effects of regime switching, distributed time delays and Lévy jumps on the dynamical behaviors, respectively.</p></abstract>

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Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey

Abstract and Applied Analysis ◽

10.1155/2009/481712 ◽

2009 ◽

Vol 2009 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Xuming Huang ◽

Xiangzeng Kong ◽

Wensheng Yang

Keyword(s):

Functional Response ◽

Prey Species ◽

Stage Structure ◽

Functional Responses ◽

Nonlinear Functional ◽

Predator Prey ◽

Prey System

We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.

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Periodicity in a neutral predator-prey system with monotone functional responses

Advances in Difference Equations ◽

10.1186/s13662-017-1101-x ◽

2017 ◽

Vol 2017 (1) ◽

Author(s):

Zhijun Zeng

Keyword(s):

Functional Responses ◽

Predator Prey ◽

Prey System

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Caching Behavior of Large Prey by Eurasian Lynx: Quantifying the Anti-Scavenging Benefits

Diversity ◽

10.3390/d12090350 ◽

2020 ◽

Vol 12 (9) ◽

pp. 350

Author(s):

Ivonne J. M. Teurlings ◽

John Odden ◽

John D. C. Linnell ◽

Claudia Melis

Keyword(s):

Observational Data ◽

Roe Deer ◽

Capreolus Capreolus ◽

Lynx Lynx ◽

Large Prey ◽

Functional Responses ◽

Eurasian Lynx ◽

Predator Prey ◽

Prey System ◽

Prey Items

Large solitary felids often kill large prey items that can provide multiple meals. However, being able to utilize these multiple meals requires that they can cache the meat in a manner that delays its discovery by vertebrate and invertebrate scavengers. Covering the kill with vegetation and snow is a commonly observed strategy among felids. This study investigates the utility of this strategy using observational data from Eurasian lynx (Lynx lynx)-killed roe deer (Capreolus capreolus) carcasses, and a set of two experiments focused on vertebrate and invertebrate scavengers, respectively. Lynx-killed roe deer that were covered by snow or vegetation were less likely to have been visited by scavengers. Experimentally-deployed video-monitored roe deer carcasses had significantly longer time prior to discovery by avian scavengers when covered with vegetation. Carcass parts placed in cages that excluded vertebrate scavengers had delayed invertebrate activity when covered with vegetation. All three datasets indicated that covering a kill was a successful caching/anti-scavenger strategy. These results can help explain why lynx functional responses reach plateaus at relatively low kill rates. The success of this anti-scavenging behavior therefore has clear effects on the dynamics of a predator–prey system.

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