• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.13-36
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• 2020

In this paper, we have presented a multispecies prey-predator harvesting system based on Lotka-Voltera model with two competing species which are affected not only by harvesting but also by the presence of a predator, the third species. We also assume that the two competing fish species releases a toxic substance to each other. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bionomic equilibrium is considered. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin's maximal principle. Finally some numerical examples are discussed to illustrate the model.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.193-207
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• 2010

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.265-285
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• 2017

In this article, a mathematical model is proposed and analyzed to study the delayed dynamics of a system having a predator and two preys with distinct growth rates and functional responses. The equilibrium points of proposed system are determined and the local stability at each of the possible equilibrium points is investigated by its corresponding characteristic equation. The boundedness of the system is established in the absence of delay and the condition for existence of persistence in the system is determined. The discrete type gestational delay of predator is also incorporated on the system. Further it is proved that the system undergoes Hopf bifurcation using delay as bifurcation parameter. This study refers that time delay may have an impact on the stability of the system. Finally Computer simulations illustrate the dynamics of the system.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.781-802
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• 2011

Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.955-967
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• 2011

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1411-1427
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• 2009

We propose a model based on Lotka-Volterra dynamics with two competing spices which are affected not only by harvesting but also by the presence of a predator, the third species. Hyperbolic and linear response functions are considered. We derive the conditions for global stability of the system using Lyapunov function. The optimal harvest policy is studied and the solution is derived in the interior equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed. The nature of variations in the two prey species and one predator species is studied extensively through graphical illustrations.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.695-713
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• 2013

We formulate and study a predator-prey model with non-monotonic functional response type and weak Allee effects on the prey, which extends the system studied by Ruan and Xiao in [Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001), no. 4, 1445-1472] but containing an extra term describing weak Allee effects on the prey. We obtain the global dynamics of the model by combining the global qualitative and bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the supercritical and the subcritical Hopf bifurcations, and the homoclinic bifurcation, as the values of parameters vary. In the generic case, the model has the bifurcation of cusp type of codimension 2 (i.e., Bogdanov-Takens bifurcation).

• Journal of the Korea Society of Computer and Information
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• v.26 no.9
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• pp.27-35
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• 2021

Artificial life is used in various fields of applied science by evaluating natural life-related systems, their processes, and evolution. Research has been actively conducted to evolve physical body design and behavioral control strategies for the dynamic activities of these artificial life forms. However, since co-evolution of shapes and neural networks is difficult, artificial life with optimized movements has only one movement in one form and most do not consider the environmental conditions around it. In this paper, artificial life that co-evolve bodies and neural networks using predator-prey models have environmental adaptive movements. The predator-prey hierarchy is then extended to the top-level predator, medium predator, prey three stages to determine the stability of the simulation according to initial population density and correlate between body evolution and population dynamics.

• Journal of the Korea Society for Simulation
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• v.22 no.3
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• pp.1-6
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• 2013

The ecosystem is the complex system consisting of various biotic and abiotic factors and the factors interact with each other in the hierarchical predator-prey relationship. Since the competitive relation spatiotemporally occurs, the initial state of population density and species distribution are likely to play an important role in the stability of the ecosystem. In the present study, we constructed a lattice model to simulate the three-trophic ecosystem (predatorprey- plant) and using the model, explored how the ecosystem stability is affected by the initial density. The size of lattice space was $L{\times}L$, (L=100) with periodic boundary condition. The initial density of the plant was arbitrarily set as the value of 0.2. The simulation result showed that predator and prey coexist when the density of predator is less than or equal to 0.4 and the density of prey is less than or equal to 0.5. On the other hand, when the predator density is more than or equal to 0.5 and the density of prey is more than or equal to 0.6, both of predator and prey were extinct. In addition, we found that the strong nonlinearity in the interaction between species was observed in the border area between the coexistence and extinction in the species density space.