Construction of Barrier in a Fishing Game With Point Capture

This paper addresses a particular pursuit-evasion game, called as “fishing game” where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived

MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES

In finite-dimensional Euclidean space, we analyze the problem of pursuit of a single evader by a group of pursuers, which is described by a system of differential equations with Caputo fractional derivatives of order $alpha.$ The goal of the group of pursuers is the capture of the evader by at least $m$ different pursuers (the instants of capture may or may not coincide). As a mathematical basis, we use matrix resolving functions that are generalizations of scalar resolving functions. We obtain sufficient conditions for multiple capture of a single evader in the class of quasi-strategies. We give examples illustrating the results obtained

The evolution of coordinated cooperative behaviors

Cooperative behaviors are useful to many species of animals. Predators may team up to hunt large prey that they cannot catch on their own, while prey can herd together for defense. This dissertation focuses on understanding the environmental factors and cognitive architectures underlying the evolution of coordinated cooperation. An agent-based neuroevolutionary simulation of an ecosystem containing teams of predators and prey was built, modeling the environment of spotted hyenas. Communication, prey-capture rewards and reward-sharing strategies were found to determine whether cooperative hunting behaviors emerged. This simulation was extended to more complex cooperative behavior, that of coordinated mobbing. Through careful coordination, a large number of spotted hyenas can attack a group of lions and successfully steal a kill, even though lions are much stronger. The computational model developed in this dissertation helped understand how spotted hyenas are able to perform this complex cooperative task and how mobbing behaviors evolved. Many factors that were observed affecting lion-hyena interaction and rates of lion-mobbing in nature were also discovered using the model. This model was then used to make predictions about real-life hyena behaviors during mobbing events, which may be verified in the field in future. These results and predictions lead to general insights into how coordinated cooperative behaviors arise in humans and animals. Such insights in turn should prove useful in building cognitive architectures and team strategies for artificial agents in the future.Computer Science