• Journal of applied mathematics & informatics
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• 제29권3_4호
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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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• 제23권1_2호
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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.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.149-158
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• 2006

In this paper, we consider the Lotka- Volterra predator-prey system, in which constant quantity of the prey is harvested in regular pulses. The ultimate behavior of the solutions starting from different regions is mainly studied. Further, some examples are given to illustrate our results.

• 충청수학회지
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• 제31권1호
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• pp.75-87
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• 2018

In this paper, we consider ratio-dependent predator-prey models with disease in the prey under Neumann boundary condition. We investigate sufficient conditions for the existence and non-existence of non-constant positive steady-state solutions by the effects of the induced diffusion rates.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.225-247
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• 2010

In this paper, we establish a two-competitive-prey and one-predator Holling type II system by introducing a proportional periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for the predator at different fixed time. We show the boundedness of the system and find conditions for the local and global stabilities of two-prey-free periodic solutions by using Floquet theory for the impulsive differential equation, small amplitude perturbation skills and comparison techniques. Also, we prove that the system is permanent under some conditions and give sufficient conditions under which one of the two preys is extinct and the remaining two species are permanent. In addition, we take account of the system with seasonality as a periodic forcing term in the intrinsic growth rate of prey population and then find conditions for the stability of the two-prey-free periodic solutions and for the permanence of this system. We discuss the complex dynamical aspects of these systems via bifurcation diagrams.

• 한국컴퓨터정보학회논문지
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• 제26권9호
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• pp.27-35
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• 2021

인공생명체 연구는 자연 생명과 관련된 시스템이나 그 과정들, 진화 등을 평가해 다양한 응용과학 분야에 활용된다. 이러한 인공생명체의 원활한 활동을 위해 물리적 신체 설계와 행동 제어전략을 진화시키는 연구가 활발히 진행되었다. 그러나 형태와 신경망을 공진화시키는 것은 어렵기에 최적화된 움직임을 가진 인공생명체는 한 가지 형태에 한 가지 움직임만을 가지며 주변 환경 상황은 고려하지 않는 것이 대부분이다. 본 논문에서는 포식자-피식자 모델을 이용하여 형태와 신경망을 공진화하는 인공생명체가 환경적응형 움직임을 갖게 한다. 그런 다음 포식자-피식자 계층 구조를 최상위 포식자-중간 포식자-최하위 피식자 3단계로 확장하여 초기 개체군 밀도에 따라 시뮬레이션의 안정성을 판별하며 형태 진화와 개체군 역학 간의 상관관계를 분석한다.

• International Journal of Industrial Entomology and Biomaterials
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• 제2권2호
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• pp.173-180
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• 2001

The stink bug, Eocanthecona furcellata (Wolff.) is a natural and potential biocontrol agent of Spilarctia obliqua (Walk.). The present investigation reveals the biology, predatory efficiency and reproductive parameters of the predator which feeds on S. obliqua caterpillars in mulberry plantation. In order to find out the role of prey sine on the biology of the predators the predatory insects were separately fed with small and large caterpillars of S. obliqua. The incubation period of the eggs of E. furcellata was 8.37${\pm}$0.44 days, while the nymphal duration varied as per the prey sine. The predator when supplied with small larvae of prey, consumed 61.1 larvae and completed nymphal stage in 19.9 days; while those fed with larger prey, consumed 36.1 larvae and completed their nymphal stage in 21.55 days. The prey size also influences the reproductive parameters of the predator, The adult female predator is more voracious feeder than the adult male and consumed 41.9${\pm}$0.64 small larvae and 42.2${\pm}$0.87 large larvae during their life span. The longevity of male and female was observed as 20.7 and 29.4 days respectively. Visualization of the predator as well as the movement of the prey increases the predatory efficiency. Scanning electron microscopic studies on the feeding part explain its support in effective predation. Field observations indicated a drastic fall in the incidence of the mulberry pest, S. obliqua with the increased population E. furcellata in mulberry plantation.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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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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• 제27권5_6호
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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 applied mathematics & informatics
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• 제29권5_6호
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• pp.1193-1204
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• 2011

In the present paper we consider a differential-algebraic prey-predator model with stage structure for prey and harvesting of predator species. Stability and instability of the equilibrium points are discussed and it is observed that the model exhibits a singular induced bifurcation when the economic profit is zero. It indicates that the zero economic profit brings impulse, i.e. rapid expansion of the population and the system collapses. For the purpose of stabilizing the system around the positive equilibrium, a state feedback controller is designed. Finally, numerical simulations are given to show the consistency with theoretical analysis.