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Due to lack of knowledge: Missing mechanisms (ignored “too small" or “too fast" or “unimportant" processes) Unresolved scales (not represented in models) Model uncertainties
The Earth shows a constant display of an organized complexity system, and its intrinsic capacity for sporadic self-organization constitutes its fundamental and profound mysterious property. A graphica...
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...
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...
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. ...
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.
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivativ...
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...
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...
Abstract: Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory s...
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...
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...
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...
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 ...

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