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Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems
typicality probability Boltzmann statistical mechanics dynamical systems ergodic epsilon-ergodic translation-continuous translation-close
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2016/6/15
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In dynamical systems theory measures can similarly be interpreted as typicality m...
Theory Reduction in Physics:A Model-Based,Dynamical Systems Approach
reduction theory reduction physics dynamical system emergence intertheory relations inter-theory relations Nagel limit
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2016/6/15
In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in ...
Evidence for the Deterministic or the Indeterministic Description?--A Critique of the Literature about Classical Dynamical Systems
determinism indeterminism randomness underdetermination ergodic theory stochatic processes dynamical systems
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2016/5/31
It can be shown that certain kinds of classical deterministic descriptions and indeterministic descriptions are observationally equivalent. In these cases there is a choice between deterministic and i...
Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE’s with a Small Parameter
Quasi linear parabolic equations parameters quasi linear initial boundary value
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2015/9/28
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
Metastability for Non-Linear Random Perturbations of Dynamical Systems
Quasi linear parabolic equation the small parameter the second order items
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2015/9/28
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding di@...
A Compactification of H′ enon Mappings in C2 as Dynamical Systems
H′ enon Mappings C2 as Dynamical Systems
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2015/8/26
A Compactification of H′ enon Mappings in C2 as Dynamical Systems.
Towards a Global Theory of Singularly Perturbed Dynamical Systems
Perturbed Dynamical System Theory
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2015/8/25
Dynamical systems with multiple time scales arise naturally in many domains.
Models of neural systems provide the principal motivation for this
paper. Most of the previous mathematical analysis of q...
A class of Lyapunov functionals for analyzing hybrid dynamical systems
Lyapunov functionals the hybrid system function hysteresis nonlinear system lyapunov functionals
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2015/8/11
In this paper, we introduce a new class of Lyapunov functionals for analyzing hybrid dynamical systems. This class can be thought of as a generalization of the Lyapunov functional introduced by Yakubo...
Control of asynchronous dynamical systems with rate constraints on events
Asynchronous dynamical systems multi-rate sys- tems Lyapunov theory linear matrix inequality bilinear matrix inequality
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2015/8/11
In this paper we consider dynamical systems which are driven by events that occur asynchronously. It is assumed that the event rates are fixed, or at least they can be bounded on any time period of le...
A Class of Lyapunov Functionals for Analyzing Hybrid Dynamical Systems
Lyapunov Functionals Analyzing Hybrid Dynamical Systems
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2015/7/10
In this paper, we introduce a new class of Lyapunov functionals for analyzing hybrid dynamical systems. This class can be thought of as a generalization of the Lyapunov functional introduced by Yakubo...
Control of Asynchronous Dynamical Systems with Rate Constraints on Events
Asynchronous dynamical systems Lyapunov theory linear matrix inequality (LMI) bilinear matrix inequality (BMI)
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2015/7/10
In this paper we consider dynamical systems which are driven by events that occur asynchronously. It is assumed that the event rates are fixed, or at least they can be bounded on any time period of le...
Shannon Meets Lyapunov: Connections between Information Theory and Dynamical Systems
Shannon Meets Lyapunov Connections between Information Theory Dynamical Systems
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2015/7/6
This paper explores connections between Information Theory, Lyapunov exponents for products of random matrices, and hidden Markov models. Specifically, we will show that entropies associated with fini...
Letting structure emerge:connectionist and dynamical systems approaches to cognition
Letting structure emerge connectionist dynamical systems
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2015/6/23
Connectionist and dynamical systems approaches explain human thought, language and behavior in terms of the emergent consequences of a large number of simple noncognitive processes. We view the entiti...
Polynomial level-set methods for nonlinear dynamical systems analysis
dynamical systems analysis level-set methods
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2015/6/19
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
Pathwise Stationar y Solutions and Random Per iodic Solutions of Random Dynamical Systems (SPDEs, Random Maps)
Pathwise Stationar y Solutions Random Per
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2015/4/3
here are two fundamental concepts in deter ministic dynamical systems: fixed
point (equilibr ium point) and per iodic solutions. For stochastic dynamical systems, they correspond to fundamental ideas...