Related papers: Variational approach for a class of cooperative sy…
The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents.…
Unitary transformations can allow one to study open quantum systems in situations for which standard, weak-coupling type approximations are not valid. We develop here an extension of the variational (polaron) transformation approach to open…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. These similarities make it possible to prove, among other results, an extinction…
Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…
Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can…
We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid…
In the past ten-fifteen years, stochastic models of continuous wave function collapse were being proposed to describe the continuous emergence of classicality from quantum. We advocate that the hybrid dynamics of canonically coupled quantum…
Aim of the paper is to study non-local dynamic boundary conditions of reactive-diffusive type for the Laplace equation from analytic and probabilistic point of view. In particular, we provide compact and probabilistic representation of the…
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions…
Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear…
In this paper we extend the investigation of cooperation in some classical evolutionary games on populations were the network of interactions among individuals is of the scale-free type. We show that the update rule, the payoff computation…
We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear…
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of…
The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…
The paper focuses on positive solutions to a coupled system of parabolic equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. By using global…