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On the Theory of Synchronization of Dynamical Systems
Differential Equations, 2018We prove theorems on the synchronization of dynamical systems with respect to all and part of the state variables in both the sense of the classical definition of synchronization (Blekhman) and the sense of Zubov; some illustrative examples are considered.
A. V. Shchennikov, V. N. Shchennikov
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Dynamical Systems in Number Theory
1982Many problems in number theory may be stated as problems relating to the uniform distribution of certain numerical sequences. Recall that the sequence x1, x2,...., 0 ≤ x n ≤ 1, is uniformly distributed on the closed interval [0, 1], if for any function f ∈ C([0, 1]) we have the relation $$ \mathop{{\lim }}\limits_{{n \to \infty }} \frac{1}{n}\sum ...
I. P. Cornfeld +2 more
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Dynamical Systems in Probability Theory
1982Suppose M is the set of all sequences, infinite in both directions x = (..., y-1, y0, y1,...), whose coordinates y i are points of a fixed measurable space (Y, 𝔄). M possesses a natural σ-algebra 𝔖 generated by cylindrical sets, i.e., sets of the form $$ A = \{ x = (...,{y_{{ - 1}}},{y_{0}},{y_{1}},...) \in M:{y_{{{i_{1}}}}} \in {C_{1}},...,{y_ ...
Yakov G. Sinai +2 more
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Dynamic Systems Control Theory. [PDF]
, 1977 Abstract : The areas of research cover a diverse spectrum for deterministic and stochastic differential games through identification and filtering all the way to system synthesis. For further information on details refer to the final report. (Author)
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Dynamical Systems Theory of Irreversibility
2005Recent work on the connections between dynamical systems theory and nonequilibrium statistical mechanics is reviewed with emphasis on results which are compatible with Liouville’s theorem. Starting from a general discussion of time-reversal symmetry in the Newtonian scheme, it is shown that the Liouvillian eigenstates associated with the Pollicott ...
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A theory for synchronization of dynamical systems
Communications in Nonlinear Science and Numerical Simulation, 2009Abstract In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented.
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Realisation theory for dynamical systems
Proceedings of the Institution of Electrical Engineers, 1979The paper is concerned with certain aspects of modelling dynamical systems. This problem can be divided into two parts; first, there is the question of identifying the system structure, and secondly of identifying the parameters defining the structure.
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