Here, we propose a mathematical model to analyze bimatrix game under entropy environment. In this new approach, the entropy function for each player are considered as objectives to the bimatrix game. This formulated model is named as Entropy Bimatrix Game Model which is a multi-objective non linear problem. To solve this kind of model, we have introduced a new solution technique, which determines the feasibility of fuzzy multiobjective non linear programming via a revised Genetic Algorithm (GA). By a real coded Genetic Algorithm, we obtained the bounds of objectives of said model and then applied fuzzy programming to determine the Nash equilibrium solution. To illustrate the methodology, numerical examples are included.

In this paper , we first extend and analyze the steepest descent method for solving optimal control problem for systems governed by Volterra integral equations . Then, we present some hybrid methods based on the extended steepest descent and two-step Newton methods, to solve the problem. The global convergence results are also established using some mild assumptions and conditions. Numerical results show that the proposed hybrid methods are more powerful and faster than the extended steepest descent method.

A new method for the solution of the generalized complementarily problem is introduced. The method is based on a no smooth equation reformulation of the generalized complementarily problem and on a no smooth Levenberg-Marquardt method for its solution. The method is shown to be globally convergent. Numerical results are also given.

This paper designs a scheme for controlling a chaotic system to a period system using active control technique. We discuss this taking chaotic Genesio system as example. We have also discussed the synchronization scheme between two different coupled chaotic systems (Genesio and Nuclear spin generator(NSG)system) as well as two identical coupled chaotic systems (Four-scroll attractor) via active control. Numerical Simulation results are presented to show the effectiveness of the proposed scheme.

This paper deals with the reliability-redundancy optimization problem considering the reliability of each component as an interval valued number that involves the selection of components with multiple choices and redundancy levels which maximize the overall system reliability subject to the given resource constraints arise on cost, volume and weight. Most of the classical mathematical methods have failed in solving the reliability-redundancy optimization problems because the objective functions as well as constraints are non-convex in nature. As an alternative to the classical mathematical methods, heuristic methods have been given much more attention by the researchers due to their easier applicability and ability to find the global optimal solutions. One of these heuristics is genetic algorithm (GA). GA is a computerized stochastic search method of global optimization based on evolutionary theory of Darwin: “The survival of the fittest” and natural genetics. Here we present GA based approach for solving interval valued mixed integer programming in reliability-redundancy optimization problem with advanced genetic operators. Finally, a numerical example has been solved and also to study the effects of changes of different GA parameters, sensitivity analyses have been carried out graphically.

This Research Paper introduces a channel aware detection (CAD) algorithm that can effectively identify the selective forwarding misbehavior from the normal channel losses. It is a special case of denial of service (DoS) attack in wireless mesh networks (WMNs) known as selective forwarding attack .The CAD algorithm is based on two strategies. With such an attack, a misbehaving mesh router just forwards a subset of packets it receives but drops the others. Channel estimation is the procedure to estimate the normal loss rate due to bad channel quality or medium access collision. Traffic monitoring is to monitor the actual loss rate, if the monitored loss rate at certain hops exceeds the estimated loss rate, those nodes involved will be identified as attackers. To determine the optimal detection thresholds that minimizes the summation of false alarm and missed detection probabilities. In this work the system is free from collision or jamming attacks, when an attacker introduces noise to simulate a noisy channel, it indeed affects the sensing process which in turn leads to inaccurate threshold. This project uses CAD approach to demonstrate the efficiency of discriminating selective forwarding attacks from normal channel losses through extensive computer simulations.

In this paper, we proposed a spline based computational simulations for solving self-adjoint singularly perturbed two-point boundary value problems. The original problem is reduced to its normal form and the reduced boundary value problem is treated by using difference approximations via cubic splines in tension. The convergence of the method is analyzed. Some numerical examples are given to demonstrate the computational efficiency of the present method.

Using the modified CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-dimensional nonlinear evolution equation. Based on the invariant group theory, Lie symmetries of the (3+1)-dimensional nonlinear evolution equation are obtained. In addition, applying the given Lie symmetry, we obtain the similarity reduction and new exact solutions, At last, we give the conservation laws of the (3+1)-dimensional nonlinear evolution equation.