• 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.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.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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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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• v.14 no.4
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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.

• 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.

• International Journal of Industrial Entomology and Biomaterials
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• v.2 no.2
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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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• 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.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 applied mathematics & informatics
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• v.29 no.5_6
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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.