Related papers: Evolutionary Dynamics and Lipschitz Maps
In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…
An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to…
We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity,…
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…
In Willems' behavioral systems theory, a dynamical system is identified with the set of all trajectories compatible with its laws of motion. In the linear time-invariant setting this trajectory set is a linear subspace, and its algebraic…
This paper addresses the problem of stochastic optimization with decision-dependent uncertainty, a class of problems where the probability distribution of the uncertain parameters is influenced by the decision-maker's actions. While recent…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
This article develops mathematical formalisms and provides numerical methods for studying the evolution of measures in nonsmooth dynamical systems using the continuity equation. The nonsmooth dynamical system is described by an evolution…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
This paper addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…
All Lipschitz dynamics with the weak infinitesimal contraction (WIC) property can be expressed as a Lipschitz nonlinear system in proportional negative feedback -- this statement, a ``structure theorem,'' is true in the $p=1$ and $p=\infty$…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…