Related papers: Selection theorem for systems with inheritance
We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under…
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…
We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force,…
For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of the…
We discuss the cosmology of axion-scalar systems in asymptotic limits of type IIB/F-theory flux compactifications. These results allow us to test a putative extension of the Distance Conjecture in a dynamical setting, which posits that…
Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…
We consider a kinetic equation describing evolution of a particle distribution function in a system with nonlinear wave-particle interactions (trappings into a resonance and nonlinear scatterings). We study properties of its solutions and…
Discrete-time regulatory networks are dynamical systems on directed graphs, with a structure inspired on natural systems of interacting units. There is a natural notion of determination amongst vertices, which we use to classify the nodes…
We apply the dynamical systems tools to study the asymptotic properties of a cosmological model based on a non-linear modification of General Relativity in which the standard Einstein-Hilbert action is replaced by one of Dirac-Born-Infeld…
We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…