Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

Wikan, Arild; Kristensen, Ørjan

doi:10.1007/s12190-020-01484-8

Cited by 5 publications

(2 citation statements)

References 40 publications

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“…For instance, Liz and Ruiz-Herrera [25] reported harvesting-induced period-bubbling transition to chaos in a one-dimensional discrete-time population model. Wikan and Kristensen [26] found, for a discrete predator-prey system, that predator harvesting can produce instability for some effort range. Our present analysis revealed that a delayed harvesting can also be destabilizing and can also result in several novel phenomena that cannot be obtained under traditional harvesting strategy.…”

Section: Discussionmentioning

confidence: 99%

Stability scenarios and period‐doubling onset of chaos in a population model with delayed harvesting

Pati

Ghosh

2023

Math Methods in App Sciences

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In this work, we investigate complete stability behaviors of the Rosenzweig-MacArthur predator-prey model with delayed harvesting of the prey. The unharvested system exhibits either a steady-state or an oscillatory dynamics for the coexistence of the species. We explore how the delayed harvesting affects the dynamics of these two modes by analyzing the system stability in effort-delay bi-parameter plane. Some novel dynamical scenarios and intricate dynamics are obtained. Analytical conditions for different stability scenarios are derived by examining the associated quasi-polynomial eigenvalue equation.For invariant harvesting effort, the time delay induces four stability scenarios: stability invariance, instability invariance, stability change, and stability switching. On the other hand, the effort instigates five stability scenarios: stability invariance, instability invariance, stability change, instability change, and instability switching, when the delay strength is fixed. Majority of literatures on harvesting reported that harvesting stabilizes predator-prey interactions. However, we will show that the delayed harvesting can destabilize the system. One of the novelties of the study is to unveil the occurrence of effort-induced chaos via period-doubling mechanism. Interestingly, the effort-induced switching phenomena and chaos do not occur for non-delayed harvesting.

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Section: Discussionmentioning

confidence: 99%

Stability scenarios and period‐doubling onset of chaos in a population model with delayed harvesting

Pati

Ghosh

2023

Math Methods in App Sciences

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“…A diffusive predator-prey models are analyzed and studied in [ 32 , 33 ], complex dynamics of these models are visualized in the presence of the predator harvesting. A density-dependent prey-predator model having the effect of harvesting is investigated in [ 34 ]. Moreover, prey-predator population model with fear and Allee effects is considered in [ 35 ].…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal solutions of a diffusive directed dynamics model with harvesting

Kamrujjaman

Keya

Bulut

et al. 2022

J. Appl. Math. Comput.

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The study considers a directed dynamics reaction-diffusion competition model to study the density of evolution for a single species population with harvesting effect in a heterogeneous environment, where all functions are spatially distributed in time series. The dispersal dynamics describe the growth of the species, which is distributed according to the resource function with no-flux boundary conditions. The analysis investigates the existence, positivity, persistence, and stability of solutions for both time-periodic and spatial functions. The carrying capacity and the distribution function are either arbitrary or proportional. It is observed that if harvesting exceeds the growth rate, then eventually, the population drops down to extinction. Several numerical examples are considered to support the theoretical results. Supplementary Information The online version contains supplementary material available at 10.1007/s12190-022-01742-x.

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Torus doubling route to chaos and chaos eradication in delayed discrete‐time predator–prey models

Ghosh

Sarda

Sahu

2022

Math Methods in App Sciences

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This paper analyses a class of discrete‐time delayed predator–prey models where time delay is incorporated into the prey's density‐dependent growth term. We explore how time delay, carrying capacity, and harvesting can generate or suppress chaotic motion. Analytical conditions for local stability of the fixed point are derived by using the Routh–Hurwitz criterion. Increasing the time delay has the great potential to change the coexisting stable fixed point to unstable via a Neimark–Sacker bifurcation. Thus, the systems may experience quasi‐periodic and chaotic motion when the coexisting fixed point is unstable. The existence of a quasi‐periodic loop, which generates a 2‐quasi‐periodic loop, and then 4, 8, and 16 quasi‐periodic loops are successively detected as the carrying capacity increases. Further increase of carrying capacity induces chaos. Thus, a torus doubling route to chaos is explored in our article, which has been relatively less reported in the existing literature. Nevertheless, we show that harvesting either prey or predator is more likely to suppress chaos and stabilize the coexisting steady state. We draw all the bifurcation diagrams when delay, carrying capacity, and harvesting strength are varied. The qualitative nature of the phase portraits is determined by computing all the Lyapunov exponents. The analysis of these delayed models in a discrete‐time framework might attract a wide range of researchers to work in this direction. In the conclusion section, we also disclose some remaining questions and future perspectives.

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Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

Cited by 5 publications

References 40 publications

Stability scenarios and period‐doubling onset of chaos in a population model with delayed harvesting

Stability scenarios and period‐doubling onset of chaos in a population model with delayed harvesting

Spatio-temporal solutions of a diffusive directed dynamics model with harvesting

Torus doubling route to chaos and chaos eradication in delayed discrete‐time predator–prey models

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