Search results for "dynamical systems theory"
showing 10 items of 126 documents
Influence of pump coherence on the dynamic behavior of a laser
1988
The dynamic behavior of a coherently pumped single-mode unidirectional ring laser with a homogeneously broadened three-level active medium is studied. Our formulation is based on a set often real equations of the plane-wave, mean-field Maxwell–Bloch type. The instability domain in the main control parameters space is determined. Our numerical study of these equations for a parameter range of the type explored in the recent experiments by Weiss Brock [ Phys. Rev. Lett.57, 2804 ( 1986)] reveals some similarities, but striking differences between our theoretical predictions and their experimental observations are also noted.
A genetic algorithm to calibrate dynamical systems: Confidence intervals for parameters and residuals
2018
This paper presents a genetic algorithm to calibrate dynamical systems that is able to calculate confidence intervals for the parameters of the system. As an application case is used to calibrate the system that reproduces the dynamical response of the General Factor of Personality (GFP) to a given stimulus, particularly to a stimulant drug dose. The model is called in Literature as the response model and includes an integro-differential equation. The presented application case is a single case ABC experimental design where the stimulus is methylphenidate.
Mechanics and self-organization in tissue development
2021
Self-organization is an all-important feature of living systems that provides the means to achieve specialization and functionality at distinct spatio-temporal scales. Herein, we review this concept by addressing the packing organization of cells, the sorting/compartmentalization phenomenon of cell populations, and the propagation of organizing cues at the tissue level through traveling waves. We elaborate on how different theoretical models and tools from Topology, Physics, and Dynamical Systems have improved the understanding of self-organization by shedding light on the role played by mechanics as a driver of morphogenesis. Altogether, by providing a historical perspective, we show how i…
Explicit Granger causality in kernel Hilbert spaces
2020
Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods, and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled R\"ossler systems, and is exploited to disclose the El Ni\~no-Southern Oscillation (ENSO) phenomenon f…
Hankelet-based dynamical systems modeling for 3D action recognition
2015
This paper proposes to model an action as the output of a sequence of atomic Linear Time Invariant (LTI) systems. The sequence of LTI systems generating the action is modeled as a Markov chain, where a Hidden Markov Model (HMM) is used to model the transition from one atomic LTI system to another. In turn, the LTI systems are represented in terms of their Hankel matrices. For classification purposes, the parameters of a set of HMMs (one for each action class) are learned via a discriminative approach. This work proposes a novel method to learn the atomic LTI systems from training data, and analyzes in detail the action representation in terms of a sequence of Hankel matrices. Extensive eval…
Statistics of nonlinear stochastic dynamical systems under Lévy noises by a convolution quadrature approach
2010
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficie…
Attractors for non-autonomous retarded lattice dynamical systems
2015
AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.
Modeling interactions between political parties and electors
2017
In this paper we extend some recent results on an operatorial approach to the description of alliances between political parties interacting among themselves and with a basin of electors. In particular, we propose and compare three different models, deducing the dynamics of their related {\em decision functions}, i.e. the attitude of each party to form or not an alliance. In the first model the interactions between each party and their electors are considered. We show that these interactions drive the decision functions towards certain asymptotic values depending on the electors only: this is the {\em perfect party}, which behaves following the electors' suggestions. The second model is an …
Implementability of Liouville Evolution, Koopman and Banach-Lamperti Theorems in Classical and Quantum Dynamics
2002
We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly formulated in terms of Jordan morphisms and isometries on non-commutative Lp spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.
Quantitative ergodicity for some switched dynamical systems
2012
International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.