Related papers: Invariant critical sets of conserved quantities
Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems…
This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle's Invariance Principle for these systems and state asymptotic stability criteria. We also present some related…
We show that invariant states of C*-dynamical systems can be approximated in the weak*-topology by invariant pure states, or almost invariant pure states, under various circumstances.
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the previous notions of self-adjoint and quasi self-adjoint…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The problem of reduced description is studied as a problem of constructing the slow…
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…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems.
The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well known discrete Painlev\'e equations $dP_{III}$,…
Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…