• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.2
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• pp.234-252
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• 2013

Due to the uncertain of connections in Delay Tolerant Networks (DTNs), most routing algorithms in DTNs need nodes to forward the message to others based on the opportunistic contact. The contact is related with the beaconing rate. In particular, nodes have more chances to encounter with each other with bigger beaconing rate, but more energy will be used. On the other hand, if the nodes forward the message to every node all the time, the efficiency of the routing algorithm is better, but it needs more energy, too. This paper tries to exploit the optimal beaconing rate and forwarding rate when the total energy is constraint. First, a theoretical framework is proposed, which can be used to evaluate the performance with different forwarding rate and beaconing rate. Then, this paper formulates a joint optimization problem based on the framework. Through Pontryagin's Maximal Principle, this paper obtains the optimal policy and proves that both the optimal forwarding and beaconing rates conform to threshold form. Simulation results show the accuracy of the theoretical framework. Extensive numerical results show that the optimal policy obtained in this paper is the best.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.387-401
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• 2006

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.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• 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.