Search results for "dynamical system"
showing 10 items of 523 documents
Information Transfer in Linear Multivariate Processes Assessed through Penalized Regression Techniques: Validation and Application to Physiological N…
2020
The framework of information dynamics allows the dissection of the information processed in a network of multiple interacting dynamical systems into meaningful elements of computation that quantify the information generated in a target system, stored in it, transferred to it from one or more source systems, and modified in a synergistic or redundant way. The concepts of information transfer and modification have been recently formulated in the context of linear parametric modeling of vector stochastic processes, linking them to the notion of Granger causality and providing efficient tools for their computation based on the state&ndash
Questions and controversies in the study of time-varying functional connectivity in resting fMRI.
2020
The brain is a complex, multiscale dynamical system composed of many interacting regions. Knowledge of the spatiotemporal organization of these interactions is critical for establishing a solid understanding of the brain’s functional architecture and the relationship between neural dynamics and cognition in health and disease. The possibility of studying these dynamics through careful analysis of neuroimaging data has catalyzed substantial interest in methods that estimate time-resolved fluctuations in functional connectivity (often referred to as “dynamic” or time-varying functional connectivity; TVFC). At the same time, debates have emerged regarding the application of TVFC analyses to re…
A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES A tribute to Ivar Bendixson
2019
In this paper one extends results of Bendixson [B] and Dumortier [D] about the germs of vector fields with an isolated singularity at the origin of IR 2 , not accumulated by periodic orbits. As new tool, one introduces minimal curves, which are curves surrounding the origin, with a minimal number of contact points with the vector field. Moreover, the arguments are essentially topological, with no use of a desingularization theory, as it is the case in [D]. 2000 Mathematics Subject Classification : 34C05, 34A26.
Estabilización de modelos económicos dinámicos con control óptimo en tiempo continuo
1990
En esta Tesis de Licenciatura se lleva a cabo el estudio de un problema determinado de optimización dinámica y sus aplicaciones en el campo de la Ciencia Económica. Un problema de optimización consiste, fundamentalmente, en la búsqueda de un extremo de una función o un funcional objetivo que proporcione un máximo o un mínimo para esa función. Cuando se habla de optimización dinámica hay que incorporar el factor tiempo al problema, en todas y cada una de las diferentes variables que intervienen, lo que afectará a los modelos matemáticos que se empleen para representar el comportamiento y las relaciones existentes entre dichas variables. También afecta al funcional objetivo a optimizar. Así, …
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
2016
A fundamental problem in the dimension theory of self‐affine sets is the construction of high‐dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high‐dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. While the existence of these equilibrium states has been well known for some years their structure has remained elusive, particularly in dimensions higher than two. In this article we give a complete description of the equilibrium states of the singular va…
Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic.
2022
This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns…
Models of the population playing the Rock-Paper-Scissors game
2018
We consider discrete dynamical systems coming from the models of evolution of populations playing rock - paper - scissors game . Asymptotic behaviour of trajectories of these systems is described, occurrence of the Neimark-Sacker bifurcation and nonexistence of time averages are proved.
On the qualitative analysis of the solutions of a mathematical model of social dynamics
2006
Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.
Identification of Replicator Mutator models
2006
The complexity of biology literally calls for quantitative tools in order to support and validate biologists intuition and traditional qualitative descriptions. In this paper, the Replicator-Mutator models for Evolutionary Dynamics are validated/invalidated in a worst-case deterministic setting. These models analyze the DNA and RNA evolution or describe the population dynamics of viruses and bacteria. We identify the Fitness and the Replication Probability parameters of a genetic sequences, subject to a set of stringent constraints to have physical meaning and to guarantee positiveness. The conditional central estimate is determined in order to validate/invalidate the model. The effectivene…
ON THE EXISTENCE OF LIMIT CYCLES IN OPINION FORMATION PROCESSES UNDER TIME PERIODIC INFLUENCE OF PERSUADERS
2008
This paper concerns a model of opinion formation in a population of interacting individuals under the influence of external leaders or persuaders, which act in a time periodic fashion. The model is formulated within a general framework inspired to a discrete generalized kinetic approach, which has been developed in Ref. 6. It is expressed by a system of non-autonomous nonlinear ordinary differential equations. The dynamics of such a system is investigated and the existence of a globally asymptotically stable periodic solution is analytically proved in three example cases, each one corresponding to a different quantitative choice of the actions of the persuaders. Equivalently, in three part…