Related papers: On a Smale Theorem and Nonhomogeneous Equilibria i…
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
The dynamics of a mathematical model of the Calvin cycle, which is part of photosynthesis, is analysed. Since diffusion of ATP is included in the model a system of reaction-diffusion equations is obtained. It is proved that for a suitable…
This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a general class of spatially homogeneous kinetic equations in space dimensions $d \geq 3$. Our results cover in particular…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution,…
Self-organized criticality is characterized by power law correlations in the non-equilibrium steady state of externally driven systems. A dynamical system proposed here self-organizes itself to a critical state with no characteristic size…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…
The flow of a $k$-cooperative system maps the set of vectors with up to~$(k-1)$ sign variations to itself. Strongly $2$-cooperative systems satisfy a strong \Poincare-Bendixson property: any bounded solution that evolves in a compact set…
We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
A nonlinear dynamical system is called eventually competitive (or cooperative) provided that it preserves a partial order in backward (or forward) time only after some reasonable initial transient. We presented in this paper the…
Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology,…
Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
We prove that for a wide family of open zooming systems and zooming potentials we have equilibrium stability, i.e., the equilibrium states depend continuously on the dynamics and the potential. We consider the open zooming systems with…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…
In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…