The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters of the...

We study the dynamics of correlation and variance in systems under the load of environmental factors. A universal effect in ensembles of similar systems under load of similar factors is described: in crisis, typically, even before obvious symptoms of crisis appear, correlation increases, and, at...

We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the...

We consider continuous-time Markov kinetics with a finite number of states and a positive equilibrium P∗. This class of systems is significantly wider than the systems with detailed balance. Nevertheless, we demonstrate that for an arbitrary probability distribution P and a general system...

We study the dynamics of correlation and variance in systems under the load of environmental factors. A universal effect in ensembles of similar systems under the load of similar factors is described: in crisis, typically, even before obvious symptoms of crisis appear, correlation increases,...

After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure concentration effects in analysis and geometry allow us to return...

In this paper, explicit method of constructing approximations (the triangle entropy method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a problem (such as, for example, rates of processes) as new...

Three results are presented. First, we prove the existence of a universal 7-cluster structure in all 143 completely sequenced bacterial genomes available in Genbank in August 2004, and explained its properties. The 7-cluster structure is responsible for the main part of sequence heterogeneity in...

Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is proven: There exists only one projector which transforms any...

In this paper, we construct low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A...