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T. K. Kar,U. K. Pahari,K. S. Chaudhuri 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2
The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.
BIFURCATIONS AND FEEDBACK CONTROL IN AN EXPLOITED PREY-PREDATOR SYSTEM WITH STAGE STRUCTURE FOR PREY
Kar, T.K.,Pahari, U.K. The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.5
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.
T. K. KAR,ASHIM BATABYAL,R. P. AGARWAL 한국산업응용수학회 2010 Journal of the Korean Society for Industrial and A Vol.14 No.1
An epidemic model with Classical Kermack-Mckendrick incidence rate under a limited resource for treatment is proposed to understand the effect of the capacity for treatment. We have assumed that treatment function is strictly increasing function of infective individuals and becomes constant when the number of infective is very large. Existence and stability of the disease free and endemic equilibrium are investigated, boundedness of the solutions are shown. Even in this simple version of the model, backward bifurcation and multiple epidemic steady states can be observed with some sets of parameter values. Hopf-bifurcation analyses are given and numerical examples are provided to help understanding.
A BIO-ECONOMIC MODEL OF TWO-PREY ONE-PREDATOR SYSTEM
Kar, T.K.,Chattopadhyay, S.K.,Pati, Chandan Kr. The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
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.
A BIOECONOMIC MODEL OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM AND OPTIMAL HARVESTING
Kar, T.K.,Misra, Swarnakamal,Mukhopadhyay, B. 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
This paper deals with the problem of a ratio-dependent prey- predator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis. Boundedness of the exploited system is examined. We derive conditions for persistence and global stability of the system. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policy is then solved by using Pontryagin's maximal principle.
KAR, T. K.,PAHARI, U. K.,CHAUDHURI, K. S. 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1
The paper deals with the problem of selective harvesting in a prey-predator model with predator self limitation. Criteria for local stability and global stability for both the exploited and unexploited system are derived. The effort has been considered as a dynamic variable and taxation as a control instrument to protect the fish populations from over exploitation. Finally, the optimal taxation policy is discussed with the help of control theory.
A bioeconomic model of a ratio-dependent predator-prey system and optimal harvesting
T. K. Kar,Swarnakamal Misra,B. Mukhopadhyay 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
This paper deals with the problem of a ratio-dependent preypredator model with combined harvesting. The existence of steady states and their stability are studied using eigenvalue analysis. Boundedness of the exploited system is examined. We derive conditions for persistence and global stability of the system. The possibility of existence of bionomic equilibria has been considered. The problem of optimal harvest policy is then solved by using Pontryagin’s maximal principle.
BIFURCATIONS AND FEEDBACK CONTROL IN AN EXPLOITED PREY-PREDATOR SYSTEM WITH STAGE STRUCTURE FOR PREY
T. K. Kar,U. K. Pahari 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.5
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.
A bio-economic model of two-prey one-predator system
T.K.Kar,S. K. Chattopadhyay,Chandan Kr. Pati 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
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. 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.
Kar, Mithilesh,Rao, P. Sudhakara,Kishore, S.,Kumar, T. Selva,Gopal, Nisha,Nayaka, A.R. Narasimha,Chandrasekaran, K. Korean Society of Sericultural Science 2009 International Journal of Industrial Entomology Vol.18 No.1
A study has been made to know the effect of a phytoecdysteroid 'Sampoorna' on uniform maturation of silkworms during spinning and its effect on diseased silkworms infected by major silkworm disease viruses, Bombyx mori nuclear polyhedrosis virus (BmNPV) and Bombyx mori infectious flacherie virus (BmIFV). In the present investigation, the effect of the phytoecdysteroid "Sampoorna" on Grasserie disease caused by BmNPV have shown an average cocoon melting of 11.91% with a disease incidence of 5.83%. The values of 't' test for different treatments of BmNPV indicated low survival rate and cocoon traits were drastically reduced. Another major disease Flacherie caused by BmIFV has shown considerable levels of larval disease incidence (22-32%) and cocoon melting (3-7.67%) with an average melting of 12.95% and 20.24% disease incidence. There is a drastic reduction in survival rate, cocoon yield and other economic traits. The control batches were indicated negligible values for disease incidence and cocoon melting with Sapoorna application and without the inoculation of the two disease-causing viruses. The application of Sampoorna on already infected batches with major pathogens triggered high mortality and disease incidence and melting percentage was also significantly increased with reduced economic traits. Hence, it is suggested that application of Sampoorna in infected batches should be done only in the extreme conditions of rearing. Application of Sampoorna on healthy batches led to uniform maturation and improvement in productivity with the added advantage of better quality cocoons and labour saving.