• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.465-472
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• 2015

In this paper, we study the existence and the stability of equilibria of predator-prey models with Ivlev's functional response. We give a simple proof for the uniqueness of limit cycles of the predator-prey system. The existence and the stability at the origin and a boundary equilibrium point(including the positive equilibrium point) are also investigated.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.575-587
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• 2006

In this paper, we provide 3 detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka-Volterra type predator-prey system. Also we obtain the sufficient conditions to ensure that the positive equilibrium point of a well known Lotka-Volterra type predator-prey system with a single discrete delay is globally asymptotically stable.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1097-1107
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• 2009

In this paper, three species stage-structured predator-prey model with time delayed and periodic constant impulsive perturbations of predator at fixed times is proposed and investigated. We show that the conditions for the global attractivity of prey(pest)-extinction periodic solution and permanence of the system. Our model exhibits a new modelling method which is applied to investigate impulsive delay differential equations. Our results give some reasonable suggestions for pest management.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.385-395
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• 2007

The dynamics of a prey-predator system, where predator population has two stages, juvenile and adult with harvesting are modelled by a system of delay differential equation. Our analysis shows that, both the delay and harvesting effort may play a significant role on the stability of the system. Numerical simulations are given to illustrate the results.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.521-533
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• 2008

We investigate a periodically forced Lotka-Volterra type predator-prey system with impulsive perturbations - seasonal effects on the prey, periodic releasing of natural enemies(predator) and spraying pesticide at the same fixed times. We show that the solutions of the system are bounded using the comparison theorems and find conditions for the stability of a stable prey-free solution and for the permanence of the system.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.19-32
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• 2020

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

• Journal of Korea Game Society
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• v.13 no.6
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• pp.27-34
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• 2013

This paper analyzes the behaviour of a prey to avoid the pursuit of a predator at predator-prey relationship to be appeared in the collective behavior of animals. One of the methods to avoid the pursuit of a predator is to rotate quickly when a predator arrives near to it. At that moment, a critical distance and a rotating angular are very important for the prey in order to survive from the pursuit, where the critical distance is the distance between the predator and the prey just before rotation. In order to analyze the critical distance and the rotating angular, this paper introduces the energy for a predator which it has at starting point of the chase and consumes during the chase. Through simulations, we can know that the rotating angle for a prey to survive from the pursuit is increased when the critical distance is shorter and when the ratio of predator's mass and prey's mass is also decreased. The results of simulations are the similar phenomenon in nature and therefore it means that the method to analyze in this paper is correct.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.29-44
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• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.27-35
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• 2021

We study the existence of positive T-periodic solutions of ratio-dependent predator-prey systems with time periodic and spatially dependent coefficients. The fixed point theorem by H. Amann is used to obtain necessary and sufficient conditions for the existence of positive T-periodic solutions.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.353-373
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• 2013

In this paper, a class of delayed predator-prey models of prey migration and predator switching is considered. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.