• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.639-651
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• 2009

In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.345-355
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• 2018

This paper looks into phase plane behavior of the solution near the positive steady-state for the system with prey density dependent response functions. The positive invariance and boundedness property of the solution to the objective model are proved. The existence result of a positive steady-state and asymptotic analysis near the positive constant equilibrium for the objective system are of interest. The results of phase plane analysis for the system are proved by observing the asymptotic properties of the solutions. Also some numerical analysis results for the behaviors of the solutions in time are provided.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.259-272
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• 2008

We are concerned with the robust control problem for the chemotaxis equations with predator-prey dynamics. That is, we present the existence and uniqueness of the solution. We also show the existence of the robust control and deduce the corresponding optimality conditions.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.87-95
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• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.164.1-164
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• 2001

Q-learning is a recent reinforcement learning algorithm that does not need a modeling of environment and it is a suitable approach to learn behaviors for autonomous agents. But when it is applied to multi-agent learning with many I/O states, it is usually too complex and slow. To overcome this problem in the multi-agent learning system, we propose the successive Q-learning algorithm. Successive Q-learning algorithm divides state-action pairs, which agents can have, into several Q-functions, so it can reduce complexity and calculation amounts. This algorithm is suitable for multi-agent learning in a dynamically changing environment. The proposed successive Q-learning algorithm is applied to the prey-predator problem with the one-prey and two-predators, and its effectiveness is verified from the efficient avoidance ability of the prey agent.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.139-151
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• 2008

We investigate a three species food chain system with Lotka-Volterra type functional response and impulsive perturbations. We find a condition for the local stability of prey or predator free periodic solutions by applying the Floquet theory and the comparison theorems and show the boundedness of this system. Furthermore, we illustrate some examples.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.273-286
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• 2005

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.35-50
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• 2007

In this work, optimal harvesting policy for the predator-prey system of three species with age-dependent and diffusion is discussed. Existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.