Search results for "dynamical system"
showing 10 items of 523 documents
Principal Poincar\'e Pontryagin Function associated to some families of Morse real polynomials
2014
It is known that the Principal Poincar\'e Pontryagin Function is generically an Abelian integral. We give a sufficient condition on monodromy to ensure that it is an Abelian integral also in non generic cases. In non generic cases it is an iterated integral. Uribe [17, 18] gives in a special case a precise description of the Principal Poincar\'e Pontryagin Function, an iterated integral of length at most 2, involving logarithmic functions with only one ramification at a point at infinity. We extend this result to some non isodromic families of real Morse polynomials.
Modelling temperature-dependent dynamics of single and mixed infections in a plant virus
2022
Multiple viral infection is an important issue in health and agriculture with strong impacts on society and the economy. Several investigations have dealt with the population dynamics of viruses with different dynamic properties, focusing on strain competition during multiple infections and the effects on viruses’ hosts. Recent interest has been on how multiple infections respond to abiotic factors such as temperature (T). This is especially important in the case of plant pathogens, whose dynamics could be affected significantly by global warming. However, few mathematical models incorporate the effect of T on parasite fitness, especially in mixed infections. Here, we investigate simple mat…
Control of irregular cardiac rhythm
2018
International audience; The aim of this work is to investigate the chaos control of the one di- mensional map which modelizes the duration of the current cardiac action potential (APD) as a function of the previous one. Using OGY control method, we obtain very satisfactory numerical results to stabilize the irregular heart rhythm into the normal rhythm.
Lag-specific transfer entropy as a tool to assess cardiovascular and cardiorespiratory information transfer
2014
In the study of interacting physiological systems, model-free tools for time series analysis are fundamental to provide a proper description of how the coupling among systems arises from the multiple involved regulatory mechanisms. This study presents an approach which evaluates direction, magnitude, and exact timing of the information transfer between two time series belonging to a multivariate dataset. The approach performs a decomposition of the well-known transfer entropy (TE) which achieves 1) identifying, according to a lag-specific information-theoretic formulation of the concept of Granger causality, the set of time lags associated with significant information transfer, and 2) assig…
O* - Dynamical Systems and * - Derivations of Unbounded Operator Algebras
1999
A spatial theory is developed for * - derivations of an algebra of unbounded operators, in terms of the concept of O*-dynamical systems. Three notions of spatiality emerge, depending on the nature of the corresponding generator. Special emphasis is put on O*-dynamical systems generated by one-parameter groups of *-automorphisms and their *-derivations.
Perturbations of the derivative along periodic orbits
2006
International audience; We show that a periodic orbit of large period of a diffeomorphism or flow, either admits a dominated splitting of a prescribed strength, or can be turned into a sink or a source by a C1-small perturbation along the orbit. As a consequence we show that the linear Poincaré flow of a C1-vector field admits a dominated splitting over any robustly transitive set.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
A Hardware and Secure Pseudorandom Generator for Constrained Devices
2018
Hardware security for an Internet of Things or cyber physical system drives the need for ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends on a lightweight and cryptographically secure random number generator. In this research work, we have introduced a new hardware chaos-based pseudorandom number generator, which is mainly based on the deletion of an Hamilton cycle within the $N$ -cube (or on the vectorial negation), plus one single permutation. We have rigorously proven the chaotic behavior and cryptographically secure property of the whole proposal: the mid-term eff…
Reduced complexity models in the identification of dynamical networks: Links with sparsification problems
2009
In many applicative scenarios it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function operating a trade-off between accuracy and complexity in the final model. We address the problem of reducing the complexity by fixing a certain degree of sparsity, and trying to find the solution that “better” satisfi…
Mathematical Modeling, Analysis, and Advanced Control of Complex Dynamical Systems
2014
1 School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia 2 Department of Engineering, Faculty of Technology and Science, University of Agder, 4898 Grimstad, Norway 3 College of Automation, Chongqing University, Chongqing 400044, China 4 School of Control Science and Engineering, Shandong University, Jinan 250061, China 5 College of Automation, Harbin Engineering University, Harbin 150001, China