Related papers: On existence and uniqueness of the carrying simple…

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…

In this paper we discuss the uniqueness of supersymmetric attractors in four dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free…

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric…

In this paper, we gives a complete classification of the global dynamics of two- species Lotka-Volterra competition models with nonlocal dispersals: where K, P represent nonlocal operators, under the assumptions that the nonlo- cal…

We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…

We study the symmetry properties of limit profiles of nonautonomous nonlinear parabolic systems with Dirichlet boundary conditions in radial bounded domains. In the case of competitive systems, we show that if the initial profiles satisfy a…

The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…

This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several fronts which we call a propagating terrace. This means,…

In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…

We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…

This paper characterizes equilibrium properties of a broad class of economic models that allow multiple heterogeneous agents to interact in heterogeneous manners across several markets. Our key contribution is a new theorem providing…

In this paper, we consider the existence and uniqueness of weak solutions of a nonlinear elliptic equation with a variable exponent, a monotonic type operator and a convection term. With the topological degree theory, we prove the existence…

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…

From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…

This thesis deals with automorphisms of real algebraic surfaces, which are polynomial transformations with a polynomial inverse. The main concern is whether their restriction to the real locus reflects all the richness of the complex…

Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…

The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…

A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting…

We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…

A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…