A prey–predator interaction under fluctuating level water

Moussaoui, Ali; Bouguima, Sidi Mohammed

doi:10.1002/mma.3055

Cited by 11 publications

(5 citation statements)

References 14 publications

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“…Therefore, such parameter is time dependent and its value follow the periodic (sinusoidal) function with lower bound greater than zero 48 . A lot of studies showed the occurrence of limit cycle oscillations through a Hopfbifurcation by varying the water level fluctuation 33,34,49,50 . However, none of the previous studies conducted for the effect of water level fluctuation showed chaotic dynamics.…”

Section: Resultsmentioning

confidence: 99%

“…Chiboub et al 32 using a two species model showed that the seasonal variations in water level of a river exert a strong influence on prey-predator interactions between pike and roach species. Moussaoui and collaborators 33,34 investigating a complex interaction between three species of fish in a lake of Southern France, showed that only under some appropriate conditions of water level the prey-predator system is permanent. Gownaris et al 22 studied the consequences of water fluctuations on ecosystem attributes of 13 African lakes.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, we investigate a complex three prey-predator system under water level fluctuations, in which the prey feeds on invertebrates, by extending the model studied by Moussaoui and Boughima 34 . Our main aim is to investigate rich dynamics including chaos, which was absent in earlier works.…”

Section: Introductionmentioning

confidence: 99%

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Chaos in a Nonautonomous Model for the Interactions of Prey and Predator With Effect of Water Level Fluctuation

et al. 2020

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Water level regulates the dynamics of different populations residing in water bodies. The increase/decrease in the level of water leads to an increase/decrease in the volume of water, which influences the interactions of fishes and catching capability. We examine how seasonal variations in water level and harvesting affect the outcome of prey–predator interactions in an artificial lake. A seasonal variation of the water level is introduced in the predation rate. We derive conditions for the persistence and extinction of the populations. Using the continuation theorem, we determine the conditions for which the system has a positive periodic solution. The existence of a unique globally stable periodic solution is also presented. Moreover, we obtain conditions for the existence, uniqueness and stability of a positive almost periodic solution. We find that if the autonomous system has a stable focus, the corresponding nonautonomous system exhibits a unique stable positive periodic solution. But, whenever the autonomous system shows limit cycle oscillations, the corresponding nonautonomous system exhibits chaotic dynamics. The chaotic behavior of system is confirmed by the positivity of the maximal Lyapunov exponent. For higher values of the assimilation fraction of prey population, the persistent oscillations of the autonomous system are eliminated and this system becomes stable. On the other hand, chaotic nature of the nonautonomous system is converted into periodicity if the assimilation fraction of prey is large. Moreover, populations behave almost periodically if the seasonally varied rate parameters are almost periodic functions of time. Our findings show that water level plays an important role in the persistence of prey–predator system.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chaos in a Nonautonomous Model for the Interactions of Prey and Predator With Effect of Water Level Fluctuation

et al. 2020

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“…The obtained results confirm the assumption that the water level fluctuations play a major role on the dynamic behavior of the prey-predator system. Very recently, Moussaoui et al, in [13] investigated a more complex interaction among three species living in the Pareloup lake under seasonal succession; the authors showed that the system is permanent under some appropriate conditions and obtained sufficient conditions which ensure the existence of the positive 1-periodic solution. The existence of periodic solutions and their stability for the delayed model of (1) are studied in [12].…”

Section: Introductionmentioning

confidence: 98%

A reaction-diffusion equations modelling the effect of fluctuating water levels on prey-predator interactions

Moussaoui

2015

Applied Mathematics and Computation

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“…Then, ( ) Φ x is called the functional response function of prey. Some scholars have devoted their efforts to investigate the predator-prey system in previous studies [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

On a predator-prey system interaction under fluctuating water level with nonselective harvesting

et al. 2020

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Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

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A prey–predator interaction under fluctuating level water

Abstract: Communicated by J. BanasiakWe consider three species system, namely prey (roach), predator (pike) and plankton. We derive persistence and extinction conditions of the populations. Using coincidence degree theory, we determine conditions for which the system has a periodic solution.

Cited by 11 publications

References 14 publications

Chaos in a Nonautonomous Model for the Interactions of Prey and Predator With Effect of Water Level Fluctuation

Chaos in a Nonautonomous Model for the Interactions of Prey and Predator With Effect of Water Level Fluctuation

A reaction-diffusion equations modelling the effect of fluctuating water levels on prey-predator interactions

On a predator-prey system interaction under fluctuating water level with nonselective harvesting

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