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This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
We show that partial dynamical symmetries (PDS) can occur at critical-points of quantum phase transitions, in which case, underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several…
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
This paper deals with the existence of asymptotic almost automorphic solution of fractional integro differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…
We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal…
New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
We study some new dynamical systems where the corresponding piecewise linear flow is neither time reversible nor measure preserving. We create a dissipative system by starting with a finite polysquare translation surface, and then modifying…
Much is known about asymptotic expansions for asymptotically normal distributions if these distributions are either absolutely continuous or pure lattice distributions. In this paper we begin an investigation of the discrete but non-lattice…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
The noncommutativity concept has wide range of applications in physical and mathematical theories. Noncommutativity in the position-time coordinates concerns the microscale structure of space-time. the noncommutativity is an intrinsic…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…