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( T. P. Mohandas ),( K. Vijayan ),( P. K. Kar ),( A. K. Awasthi ),( B. Saratchandra ) 한국잠사학회 2007 International Journal of Industrial Entomology Vol.8 No.2
Genetic diversity within the natural populations of Daba ecorace of Antheraea mylitta Drury was studied using individual silkworms collected from the South Singhbhum district of Jharkhand state of India with 21 inter simple sequence repeat (ISSR) primers. A total of 148 bands were produced, of which 79% was polymorphic. The pair wise genetic distance among the individuals varied from 0.186 to 0.329. The dendrogram grouped the individuals into 3 major clusters. Nei`s heterozygosity analysis revealed 0.265±0.18 variability within the population. The high genetic variability present within the natural population of Daba ecorace of A. mylitta is indicative of their adaptational strategy in nature and have much importance for in situ conservation as well as utilization in breeding programs.
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.
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.
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 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.
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.
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.
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.
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.