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Conditioned Likelihoods Using Bifurcation Continuation in Inverse Modeling of Dynamical Systems
Conditioned Likelihoods Bifurcation Continuation Inverse Modeling Dynamical Systems
2012/11/23
The Morris-Lecar (ML) model has applications to neuroscience and cognition. A simple network consisting of a pair of synaptically coupled ML neurons can exhibit a wide variety of deterministic behavio...
Construction of exact invariants of time-dependent linear nonholonomic dynamical systems
invariant Lie algebraic method linear nonholonomic Hamiltonian system
2012/8/8
In this work, we build exact dynamical invariants for time-dependent, linear, nonholo-
nomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into
the theoretical un...
Banach representations and affine compactifications of dynamical systems
affine compactification affine flow Asplund space enveloping semigroup non-sensitivity right topological semigroup
2012/4/18
To every Banach space V we associate a compact right topological affine semigroup E(V). We show that a separable Banach space V is Asplund if and only if E(V) is metrizable, and it is Rosenthal (i.e. ...
Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems
Lyapunov exponents the volume growth of boundary distortion the action of dynamical systems
2012/4/17
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.
Morse decomposition for random dynamical systems
Random dynamical system Morse decomposition random attractor
2011/10/18
It is well-known that Morse decomposition is very useful to study the inner structure of invariant sets for given dynamical systems. Recently, Morse decomposition is established for random dynamical s...
Morse decomposition and Lyapunov functions for dynamical systems
Differential equation and dynamical system Morse decomposition Lyapunov function
2011/10/18
In this paper, we review Morse decomposition and Lyapunov functions. Most of the results are due to Conley and are known. Attractor-repeller pairs and Morse decompositions are very useful to study the...
Variational Gaussian Process Dynamical Systems
Gaussian Dynamical Systems Machine Learning
2011/10/9
Abstract: High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphi...
Moderate Deviation Principle for dynamical systems with small random perturbation
Freidlin-Wentzell’s theorem large deviations moderate deviations Talagrand’s transportation inequality
2011/9/14
Abstract: Consider the stochastic differential equation in $\rr^d$
dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t
X^{\e}_0&=x_0,\quad x_0\in\rr^d
where $b:\rr^d\rightarrow\rr^d$ is $C^1$ s...
Controller Synthesis for Robust Invariance of Polynomial Dynamical Systems using Linear Programming
Controller Synthesis Robust Invariance Polynomial Dynamical Systems Linear Programming
2011/8/30
Abstract: In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synth...
Integral Value Transformations: A Class of Discrete Dynamical Systems
Discrete Dynamical Systems Topological Dynamics integral value Transformations
2011/9/29
Abstract: Here the Integral Value Transformations (IVTs) are considered to be Discrete Dynamical System map in the space\mathbb{N}_(0). In this paper, the dynamics of IVTs is deciphered through the li...
Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic ...
Some Results on the Information Loss in Dynamical Systems
Dynamical Systems Information Loss Results
2011/7/7
In this work we investigate the information loss in (nonlinear) dynamical input-output systems and provide some general results. In particular, we present an upper bound on the information loss rate, ...
Polytopic Invariant Verification and Synthesis for Polynomial Dynamical Systems via Linear Programming
Polytopic Invariant Verification Synthesis for Polynomial Dynamical Systems Linear Programming
2011/1/18
This paper deals with the veri cation and the synthesis of polytopic invariant sets for
polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state
space such that ...
Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
Quantum-to-Classical Correspondence Hubbard-Stratonovich Dynamical Systems
2011/3/2
We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-St...
A note on dynamical systems defining Jacobi's theta-constants
Jacobi’s theta-constants modular forms Poisson structures
2010/12/28
We propose a system of ordinary differential equations which defines Jacobi’s theta-constant series. The relations of this system to the classical Darboux–Halphen equations and equations introduced by...