• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.503-514
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• 2008

We investigate a three-species food chain system with Lotka-Volterra functional response and impulsive perturbations. In [23], Zhang and Chen have studied the system. They have given conditions for extinction of lowest-level prey and top predator and considered the local stability of lower-level prey and top predator eradication periodic solution. However, they did not give a condition for permanence, which is one of important facts in population dynamics. In this paper, we establish the condition for permanence of the three-species food chain system with impulsive perturbations. In addition, we give some numerical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.2
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• pp.129-138
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• 2013

A spatio-temporal models as systems of ODE which describe two-species Beddington - DeAngelis type predator-prey system living in a habitat of two identical patches linked by migration is investigated. It is assumed in the model that the per capita migration rate of each species is influenced not only by its own but also by the other one's density, i.e. there is cross diffusion present. We show that a standard (self-diffusion) system may be either stable or unstable, a cross-diffusion response can stabilize an unstable standard system and destabilize a stable standard system. For the diffusively stable model, numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross migration response is an important factor that should not be ignored when pattern emerges.

• 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.

• Journal of Ecology and Environment
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• v.31 no.2
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• pp.89-95
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• 2008

Sensing the approach of a predator is critical to the survival of prey, especially when the prey has no choice but to escape at a precisely timed moment. Escape behavior has been approached from both proximate and ultimate perspectives. On the proximate level, empirical research about electrophysiological mechanisms for detecting predators has focused on vision, an important modality that helps prey to sense approaching danger. Studies of looming-sensitive neurons in locusts are a good example of how the selective sensitivity of nervous systems towards specific targets, especially approaching objects, has been understood and realistically modeled in software and robotic systems. On the ultimate level, general optimality models have provided an evolutionary framework by considering costs and benefits of visually elicited escape responses. A recent paper showed how neural network models can be used to understand the evolution of visually mediated antipredatory behaviors. We discuss this new trend towards integration of these relatively disparate approaches, the proximate and the ultimate perspectives, for understanding of the evolution of behavior of predators and prey. Focusing on one of the best-studied escape pathway models, the Orthopteran LGMD/DCMD pathway, we discuss how ultimate-level optimality modeling can be integrated with proximate-level studies of escape behaviors in animals.

• 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.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.1
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• pp.86-93
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• 2012

This paper presents a new approach to solve the pursuit problem based on a univector field method. In our proposed method, a set of eight agents works together instantaneously to find suitable moving directions and follow the univector field to pursue and capture a prey agent by surrounding it from eight directions in an infinite grid-world. In addition, a set of strategies is proposed to make the pursuit problem more realistic in the real world environment. This is a general approach, and it can be extended for an environment that contains static or moving obstacles. Experimental results show that our proposed algorithm is effective for the pursuit problem.