Enrico Valdinoci – författare

This monograph introduces a new mathematical model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility.  Its main feature is the expansion of the family of Lotka-Volterra systems by introducing a new term that defines aggression.  Because the model is flexible, it can be applied to various scenarios in the context of human populations, such as strategy games, competition in the marketplace, and civil wars.

Drawing from a variety of methodologies within dynamical systems, ODEs, and mathematical biology, the authors'' approach focuses on the dynamical properties of the system. This is accomplished by detecting and describing all possible equilibria, and analyzing the strategies that may lead to the victory of the aggressive population. Techniques typical of two-dimensional dynamical systems are used, such as asymptotic behaviors regulated by the Poincaré–Bendixson Theorem.

A New Lotka-Volterra Model of Competition With Strategic Aggression will appeal to researchers and students studying population dynamics and dynamical systems, particularly those interested in the cross section between mathematics and ecology.

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.  It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods.  The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered.  The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'''' in Cetraro, June 2–7, 2014, should help to encourage further research in the area.  The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary.

The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.