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Sapna Devi - One of the best experts on this subject based on the ideXlab platform.

  • Effects of prey refuge on a ratio-dependent Predator–prey model with stage-structure of prey Population
    Applied Mathematical Modelling, 2013
    Co-Authors: Sapna Devi
    Abstract:

    Abstract In this paper, a stage-structured Predator–prey model is proposed and analyzed to study how the type of refuges used by prey Population influences the dynamic behavior of the model. Two types of refuges: those that protect a fixed number of prey and those that protect a constant proportion of prey are considered. Mathematical analyses with regard to positivity, boundedness, equilibria and their stabilities, and bifurcation are carried out. Persistence condition which brings out the useful relationship between prey refuge parameter and maturation time delay is established. Comparing the conclusions obtained from analyzing properties of two types of refuges using by prey, we observe that value of maturation time at which the prey Population and hence Predator Population go extinct is greater in case of refuges which protect a constant proportion of prey.

  • effects of prey refuge on a ratio dependent Predator prey model with stage structure of prey Population
    Applied Mathematical Modelling, 2013
    Co-Authors: Sapna Devi
    Abstract:

    Abstract In this paper, a stage-structured Predator–prey model is proposed and analyzed to study how the type of refuges used by prey Population influences the dynamic behavior of the model. Two types of refuges: those that protect a fixed number of prey and those that protect a constant proportion of prey are considered. Mathematical analyses with regard to positivity, boundedness, equilibria and their stabilities, and bifurcation are carried out. Persistence condition which brings out the useful relationship between prey refuge parameter and maturation time delay is established. Comparing the conclusions obtained from analyzing properties of two types of refuges using by prey, we observe that value of maturation time at which the prey Population and hence Predator Population go extinct is greater in case of refuges which protect a constant proportion of prey.

Joydev Chattopadhyay - One of the best experts on this subject based on the ideXlab platform.

  • A systematic study of autonomous and nonautonomous Predator–prey models with combined effects of fear, migration and switching
    Nonlinear Dynamics, 2021
    Co-Authors: Pankaj Kumar Tiwari, Sudip Samanta, Kawkab Abdullah Nabhan Al Amri, Qamar Jalil Ahmad Khan, Joydev Chattopadhyay
    Abstract:

    In this paper, we study the dynamics of a Predator–prey system under the combined effects of fear, migration and switching phenomena. This study is new in the sense that the dynamics of such system was studied either through fear or migration, or switching, but the combined effects of such three factors are yet to be explored. We observe oscillatory behavior of the system in the absence of fear, migration and switching, whereas the system shows stable dynamics if anyone of these three factors is introduced. After analyzing the behavior of system with fear, migration and switching, we find that the system does not possess periodic solution whenever the Predator Population experiences intraspecies competition, but in the absence of intraspecies competition among Predator Population, fear of Predators destabilizes the system, whereas on increasing the migration rates, the system first undergoes subcritical Hopf-bifurcation and then supercritical Hopf-bifurcation settling the system to stable coexistence. Existence of multiple limit cycles is also observed. Our results show that switching behavior of Predator Population supports the survival of prey and Predator Populations. We extend our model by assuming the fear parameters as time dependent. We find that the nonautonomous system exhibits periodic solutions, whereas the corresponding autonomous system shows stable focus. Moreover, we observe that if the autonomous system undergoes a Hopf-bifurcation through limit cycle oscillations, the corresponding nonautonomous system shows higher periodic solutions. Almost periodic behavior of the system is also observed by setting the fear parameters as almost periodic functions of time.

  • Dynamical Effects of Anti-Predator Behaviour of Adult Prey in a Predator-Prey Model with Ratio-dependent Functional Response
    Journal of Mathematics and Physics, 2017
    Co-Authors: Prabir Panja, Shyamal Kumar Mondal, Joydev Chattopadhyay
    Abstract:

    In this paper, a three species Predator-prey model has been developed. Here we divide the prey Population into two subPopulations such as $(i)$ juvenile prey and $(ii)$ adult prey Population along with only one Predator Population. It is considered that only adult prey has the anti-Predator behaviour. In this paper, two functional responses of Predator due to adult and juvenile prey have been introduced on the basis of ratio-dependency. Then the existence condition and boundedness of solution of our proposed mathematical model have been discussed. Also, the different equilibrium points and the stability condition of the system around these equilibrium points have been analyzed. After that, the extinction condition of the prey and Predator Populations and the effect of anti-Predator behaviour on the Predator Population have been explored. The global stability condition of the proposed system around the positive equilibrium point has been also discussed. Finally, some numerical simulations have been given to test our theoretical results.

  • A cannibalistic eco-epidemiological model with disease in Predator Population
    Journal of Applied Mathematics and Computing, 2017
    Co-Authors: Santosh Biswas, Sudip Samanta, Joydev Chattopadhyay
    Abstract:

    In this present article, we propose and analyze a cannibalistic Predator–prey model with disease in the Predator Population. We consider two important factors for the dynamics of Predator Population. The first one is governed through cannibalistic interaction, and the second one is governed through the disease in the Predator Population via cannibalism. The local stability analysis of the model system around the biologically feasible equilibria are investigated. We perform global dynamics of the model using Lyapunov functions. We analyze and compare the community structure of the system in terms of ecological and disease basic reproduction numbers. The existence of Hopf bifurcation around the interior steady state is investigated. We also derive the sufficient conditions for the permanence and impermanence of the system. The study reveals that the cannibalism acts as a self-regulatory mechanism and controls the disease transmission among the Predators by stabilizing the Predator–prey oscillations.

  • Effect of multiple delays on the dynamics of cannibalistic prey–Predator system with disease in both Populations
    International Journal of Biomathematics, 2017
    Co-Authors: Santosh Biswas, Sudip Samanta, Qamar J. A. Khan, Joydev Chattopadhyay
    Abstract:

    In the present paper, we investigate a prey–Predator system with disease in both prey and Predator Populations and the Predator Population is cannibalistic in nature. The model is extended by introducing incubation delays in disease transmission terms. Local stability analysis of the system around the biologically feasible equilibria is studied. The bifurcation analysis of the system around the interior equilibrium is also studied. The sufficient conditions for the permanence of the system are derived in the presence of delays. We observe that incubation delays have the ability to destabilize the cannibalistic prey–Predator system. Finally, we perform numerical experiments to substantiate our analytical findings.

  • A strategy for a disease-free system- an eco-epidemiological model based study
    Journal of Applied Mathematics and Computing, 2016
    Co-Authors: Krishna Pada Das, Sudip Samanta, Santosh Biswas, Ali Saleh Alshomrani, Joydev Chattopadhyay
    Abstract:

    The present paper deals with an eco-epidemiological model consisting of susceptible prey, infected prey and Predator. We assume that the recruitment of prey follows the saturating functional form due to habitat saturation. We make a general assumption of the non-restricted conversion rate of the Predator Population due to consumption of the infected prey Population. We study the existence and stability criteria of the equilibrium points. Our results suggest that the Predator Population may be eliminated from the system due to the negative effect of infected prey; however, the negative impact can be buffered by the alternative food. Alternative food helps Predator Population to survive and makes the system disease free. The outcomes from the model are verified numerically by taking a set of biologically feasible parameter values.

Peter A. Abrams - One of the best experts on this subject based on the ideXlab platform.

  • Harvesting creates ecological traps: consequences of invisible mortality risks in Predator-prey metacommunities.
    Ecology, 2012
    Co-Authors: Peter A. Abrams, Lasse Ruokolainen, Brian J. Shuter, Kevin S. Mccann
    Abstract:

    Models of two-patch Predator-prey metacommunities are used to explore how the global Predator Population changes in response to additional mortality in one of the patches. This could describe the dynamics of a Predator in an environment that includes a refuge area where that Predator is protected and a spatially distinct ("risky") area where it is harvested. The Predator's movement is based on its perceived fitness in the two patches, but the risk from the additional mortality is potentially undetectable; this often occurs when the mortality is from human harvesting or from a novel type of top Predator. Increases in undetected mortality in the risky area can produce an abrupt collapse of either the refuge Population or of the entire Predator Population when the mortality rate exceeds a threshold level. This is due to the attraction of the risky patch, which has abundant prey due to its high Predator mortality. Extinction of the refuge Predator Population does not occur when the refuge patch has a higher maximum per capita Predator growth rate than the exploited patch because the refuge is then more attractive when the Predator is rare. The possibility of abrupt extinction of one or both patches from high densities in response to a small increase in harvest is often associated with alternative states. In such cases, large reductions in mortality may be needed to avoid extinction in a collapsing Predator Population, or to reestablish an extinct Population. Our analysis provides a potential explanation for sudden collapses of harvested Populations, and it argues for more consideration of adaptive movement in designing protected areas.

  • Adaptive changes in prey vulnerability shape the response of Predator Populations to mortality
    Journal of theoretical biology, 2009
    Co-Authors: Peter A. Abrams
    Abstract:

    Simple models are used to explore how adaptive changes in prey vulnerability alter the Population response of their Predator to increased mortality. If the mortality is an imposed harvest, the change in prey vulnerability also influences the relationship between harvest effort and yield of the Predator. The models assume that different prey phenotypes share a single resource, but have different vulnerabilities to the Predator. Decreased vulnerability is assumed to decrease resource consumption rate. Adaptive change may occur by phenotypic changes in the traits of a single species or by shifts in the abundances of a pair of coexisting species or morphs. The response of the Predator Population is influenced by the shape of the Predator's functional response, the shape of resource density dependence, and the shape of the tradeoff between vulnerability and food intake in the prey. Given a linear Predator functional response, adaptive prey defense tends to produce a decelerating decline in Predator Population size with increased mortality. Prey defense may also greatly increase the range of mortality rates that allow Predator persistence. If the Predator has a type-2 response with a significant handling time, adaptive prey defense may have a greater variety of effects on the Predator's response to mortality, sometimes producing alternative attractors, Population cycles, or increased mean Predator density. Situations in which there is disruptive selection on prey defense often imply a bimodal change in yield as a function of harvesting effort, with a minimum at intermediate effort. These results argue against using single-species models of density dependent growth to manage Predatory species, and illustrate the importance of incorporating anti-Predator behavior into models in applied Population ecology.

  • The impact of mortality on Predator Population size and stability in systems with stage-structured prey.
    Theoretical population biology, 2005
    Co-Authors: Peter A. Abrams, Christopher Quince
    Abstract:

    The relationships between a Predator Population's mortality rate and its Population size and stability are investigated for several simple Predator-prey models with stage-structured prey Populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's Population growth; the nature of stage-transitions; and the stage-selectivity of the Predator. Instability occurs at high, rather than low Predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey Populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable Predator Population to increase in abundance as its own mortality rate increases in stable systems, provided that the Predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in Predator Population size with increasing Predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but Population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in Population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.

  • The effect of adaptive change in the prey on the dynamics of an exploited Predator Population
    Canadian Journal of Fisheries and Aquatic Sciences, 2005
    Co-Authors: Peter A. Abrams, Hiroyuki Matsuda
    Abstract:

    Mathematical models examine the relationship between harvesting effort and stock size for a Predator spe- cies when the prey adapts to the risk of predation. In one set of models, the prey can increase its own reproductive rate if it increases its vulnerability to the Predator. In the second set of models, each of two prey species has fixed characteristics, but changes in the average characteristics within the prey trophic level occur via shifts in the relative abundance of the two species. In both models, the equilibrium Predator Population can increase as harvest of that spe- cies increases. In the case of two-prey models, the Predator's equilibrium Population always increases with an increased harvest rate if the two prey coexist and share a single resource. The Predator's equilibrium Population often decreases from its maximum size to zero over a very small range of harvest rates, once those rates become high enough. Because increased stock size is often used to justify increased harvest rates, this relationship poses a risk that harvest rate will increase to the point where the stock quickly collapses. The results are relevant to understanding changes in the popu- lation size of a species experiencing declining environmental conditions. Resume : Des modeles mathematiques examinent la relation qui existe entre l'effort de recolte et la taille du stock chez une espece predatrice lorsque la proie s'adapte au risque de predation. Dans une premiere serie de modeles, la proie peut augmenter son propre taux de reproduction si sa vulnerabilite au predateur augmente. Dans une seconde serie de modeles, chacune de deux especes de proies possede des caracteristiques fixes, mais les changements dans les caracteristiques moyennes au niveau trophique des proies se font au moyen de modifications dans l'abondance relative des deux especes. Dans les deux modeles, la Population d'equilibre du predateur peut croitre a mesure que la recolte de l'espece augmente. Dans le cas du modele a deux proies, la Population d'equilibre du predateur augmente toujours en fonction de la recolte si les deux proies coexistent et partagent une meme et unique ressource. La Population d'equilibre du predateur diminue souvent de sa taille maximale a zero sur une gamme tres restreinte de taux de recolte, une fois que les taux ont atteint une certaine valeur. Parce que l'augmentation des stocks sert souvent a justifier une augmentation de la recolte, cette relation entraine le risque que le taux de recolte augmente au point que le stock s'effondre rapidement. Ces resultats sont d'interet pour comprendre les changements dans la taille de la Population chez une espece qui subit un declin des conditions de son environnement. (Traduit par la Redaction) Abrams and Matsuda 766

Ahmed Alsaedi - One of the best experts on this subject based on the ideXlab platform.

  • Dynamics of a stochastic Predator–prey model with distributed delay and Markovian switching
    Physica A: Statistical Mechanics and its Applications, 2019
    Co-Authors: Qun Liu, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi
    Abstract:

    Abstract In this paper, we study a stochastic Predator–prey model with distributed delay and Markovian switching. Firstly, we obtain sufficient criteria for weak persistence of the Predator Population. Then in the case of weak persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. Finally, we establish sufficient conditions for extinction of the Predator Population.

  • Stationary distribution and extinction of a stochastic Predator–prey model with herd behavior
    Journal of the Franklin Institute, 2018
    Co-Authors: Qun Liu, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi
    Abstract:

    Abstract In this paper, we propose and study a stochastic Predator–prey model with herd behavior. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the Predator Population in two cases, that is, the first case is the prey Population survival and the Predator Population extinction; the second case is all the prey and Predator Populations extinction. Finally, some examples together with numerical simulations are introduced to illustrate the theoretical results.

Daqing Jiang - One of the best experts on this subject based on the ideXlab platform.