A New Lotkavolterra Model Of Competition With Strategic Aggression Civil Wars When Strategy Comes Into Play 2024th Edition Elisa Affili by Elisa Affili, Serena Dipierro, Luca Rossi, Enrico Valdinoci 9783031672101, 9783031672095, 3031672100, 3031672097 instant download after payment.

In this monograph, we introduce a new model in population dynamics that describes two species, or communities, sharing the same environmental resources in a situation of open hostility. Though the main methodology fits into the broad realm of mathematical biology, relying on methods from dynamical systems, ordinary differential equations, optimization, and optimal control, the model proposed and the results presented here are completely new. The model is deduced from basic principles, accounting for competition and hostility between two species sharing the same environment. The fact of sharing this environment constitutes one of the salient features of the model in the description of a situation that, for human populations, is typical of civil wars. The model is also adapted to describe economic situations where two companies compete for the same market. Our key assumption is that one of the two populations deliberately seeks for hostility through “targeted attacks.” Hence the interaction is described not in terms of random encounters but rather via the strategic decisions of one population that can attack the other according to different levels of aggressiveness. This leads to a non-variational model for the two populations in conflict, taking into account structural parameters such as the relative fit of the two populations with respect to the available resources and the effectiveness of the attack strikes of the aggressive population. One of the features that distinguishes this model from usual competitive systems is that it allows one of the population to go extinct in finite time. The analysis that we perform focuses on the dynamical properties of the system, by detecting and describing all possible equilibria and their basins of attraction. Moreover, we analyze the strategies that may lead to the victory of the aggressive population, i.e., the choice of the aggressiveness parameter, in dependence of the structural constants of the system and possibly varying…