Rich dynamics in a stochastic predator-prey model with protection zone for the prey and multiplicative noise applied on both species

Belabbas, Mustapha; Ouahab, Abdelghani; Souna, Fethi

doi:10.1007/s11071-021-06903-4

Cited by 19 publications

(6 citation statements)

References 42 publications

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“…According to simulation results, these parametric restrictions will not hold for large-amplitude environmental noise. Consequently, it can destabilize the system, and, in that case, no stationary distribution can be found 32 , 47 . As a result of the existence of stationary distributions, there can be some degree of stochastic stability.…”

Section: Discussionmentioning

confidence: 99%

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Schooling behavior driven complexities in a fear-induced prey–predator system with harvesting under deterministic and stochastic environments

Pal

2023

Sci Rep

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The well-being of humans is closely linked to the well-being of species in any ecosystem, but the relationship between humans and nature has changed over time as societies have become more industrialized. In order to ensure the future of our ecosystems, we need to protect our planet’s biodiversity. In this work, a prey–predator model with fear dropping prey’s birth as well as death rates and nonlinear harvesting, is investigated. In addition, we consider that the consumption rate of predators, i.e., the functional response, is dependent on schooling behavior of both species. We have investigated the local stability of the equilibrium points and different types of bifurcations, such as transcritical, saddle-node, Hopf and Bogdanov–Takens (BT). We find that consumption rate of predator, fear and harvesting effort give complex dynamics in the neighbourhood of BT-points. Harvesting effort has both stabilizing and destabilizing effects. There is bistability between coexistence and predator-free equilibrium points in the system. Further, we have studied the deterministic model in fluctuating environment. Simulation results of stochastic system includes time series solutions of one simulation run and corresponding phase portraits. Notably, several simulation runs are conducted to obtain time series solutions, histograms, and stationary distributions. Our findings exhibit that during stochastic processes, model species fluctuate around some average values of the deterministic steady-state for lower environmental disturbances. However, higher values of environmental disturbances lead the species to extinction.

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Section: Discussionmentioning

confidence: 99%

“…Thus, prey–predator models cannot ignore the shifting environmental effects, whereas stochastic models can accurately predict dynamics when the environment changes 22 . Belabbas et al 32 investigated a new approach of a stochastic prey–predator model with protection zone for the prey and found rich dynamics of the system.…”

Section: Introductionmentioning

confidence: 99%

Schooling behavior driven complexities in a fear-induced prey–predator system with harvesting under deterministic and stochastic environments

Pal

2023

Sci Rep

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“…Through this work, we developed a stochastic analysis of an integrative cancer model, by finding relations between relevant parameters and eventual biological fluctuations. Particularly, we studied the influence of multiplicative and demographic noise, commonly used in biological systems [39][40][41][42], in an integrative cancer model for different fractions of birth and death rates. We observed that for some combinations of demographic rates and noise intensity, the total amount of cancer cells is lower than the amount in basal conditions.…”

Section: Discussionmentioning

confidence: 99%

Stochastic and parameter analysis for an integrative cancer model

Reale¹,

Margarit²,

Scagliotti³

et al. 2022

Phys. Scr.

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In previous work, we presented a model that integrates cancer cell differentiation and immunotherapy, analysing a particular therapy against cancer stem cells by cytotoxic cell vaccines. As every biological system is exposed to random fluctuations, is important to incorporate stochasticity in the models to adequate their behaviour to experimental observations. Thus, we propose a necessary upgrade to the former model incorporating fluctuations in it. On the one hand, we added multiplicative noise throughout the proposed system, and on the other, we specifically analysed the influence of demographic and multiplicative noise on the parameters of reproduction and death in cancer cells. In both cases, we studied the dynamics for different values of the parameters involved. It was observed that the final number of cancer cells decreases for different combinations of these parameters and noise intensity.

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“…In order to capture these fluctuations, we introduce the multiplicative white noise terms into (3). As in Sengupta et al, Bodine and Yust, and Srinivasu et al [27,29,30], we now suppose that the intrinsic growth rate of prey and the death rate of predator are mainly affected by environmental noise such that…”

Section: Stochastic Analysis the Stochastic Model Formulationmentioning

confidence: 92%

Stochastic time-optimal control and sensitivity studies for additional food provided prey-predator systems involving Holling type-IV functional response

Prakash

Vamsi

2023

Front. Appl. Math. Stat.

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In this study we consider an additional food provided prey-predator model exhibiting Holling type-IV functional response incorporating the combined effects of both the continuous white noise and discontinuous Lévy noise. We prove the existence and uniqueness of global positive solutions for the proposed model. We perform the stochastic sensitivity analysis for each of the parameters in a chosen range. Later we do the time optimal control studies with respect quality and quantity of additional food as control variables. Making use of the arrow condition of the sufficient stochastic maximum principle, we characterize the optimal quality of additional food and optimal quantity of additional food. We then perform the sensitivity of these control variables with respect to each of the model parameters. Numerical results are given to illustrate the theoretical findings with applications in biological conservation and pest management. At the end we briefly study the influence of the noise on the dynamics of the model.

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Rich dynamics in a stochastic predator-prey model with protection zone for the prey and multiplicative noise applied on both species

Cited by 19 publications

References 42 publications

Schooling behavior driven complexities in a fear-induced prey–predator system with harvesting under deterministic and stochastic environments

Schooling behavior driven complexities in a fear-induced prey–predator system with harvesting under deterministic and stochastic environments

Stochastic and parameter analysis for an integrative cancer model

Stochastic time-optimal control and sensitivity studies for additional food provided prey-predator systems involving Holling type-IV functional response

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