Search results for "attractor"
showing 10 items of 162 documents
Dynamical Models of Interrelation in a Class of Artificial Networks
2020
The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.
Language in Complexity. The Emerging Meaning
2017
This contributed volume explores the achievements gained and the remaining puzzling questions by applying dynamical systems theory to the linguistic inquiry. In particular the book is divided into three parts, each one addressing of the following topics: a) Facing complexity in the right way: mathematics and complexity; b) Complexity and theory of language; c) From empirical observation to formal models: investigations of specifici linguistic phenomena, like enunciation, deixis, or the meaning of the metaphorical phrases.
Graphical Structure of Attraction Basins of Hidden Chaotic Attractors : The Rabinovich-Fabrikant System
2019
The attraction basin of hidden attractors does not intersect with small neighborhoods of any equilibrium point. To the best of our knowledge this property has not been explored using realtime interactive three-dimensions graphics. Aided by advanced computer graphic analysis, in this paper, we explore this characteristic of a particular nonlinear system with very rich and unusual dynamics, the Rabinovich–Fabrikant system. It is shown that there exists a neighborhood of one of the unstable equilibria within which the initial conditions do not lead to the considered hidden chaotic attractor, but to one of the stable equilibria or are divergent. The trajectories starting from any neighborhood o…
Boolean Networks: A Primer
2021
Abstract Autism Spectrum Disorders (ASDs) stand out as a relevant example where omics-data approaches have been extensively and successfully employed. For instance, an outstanding outcome of the Autism Genome Project relies in the identification of biomarkers and the mapping of biological processes potentially implicated in ASDs’ pathogenesis. Several of these mapped processes are related to molecular and cellular events (e.g., synaptogenesis and synapse function, axon growth and guidance, etc.) that are required for the development of a correct neuronal connectivity. Interestingly, these data are consistent with results of brain imaging studies of some patients. Despite these remarkable pr…
Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation
2013
From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attracto…
Hidden attractors on one path : Glukhovsky-Dolzhansky, Lorenz, and Rabinovich systems
2017
In this report, by the numerical continuation method we visualize and connect hidden chaotic sets in the Glukhovsky-Dolzhansky, Lorenz and Rabinovich systems using a certain path in the parameter space of a Lorenz-like system.
The fabric attractor
1997
Abstract The nature of fabric accumulation in high strain zones such as ductile shear zones depends on the nature and orientation of flow eigenvectors or apophyses. Some flow apophyses can act as ‘attractors’ of material lines or principal finite strain axes. This paper explains the nature of such attractors and discusses their significance and orientation in different monoclinic flow types. In ductile shear zones, strain values are high enough to show the effect of attractors in deformed rocks clearly. The concept of attractors can be used in deformation modelling, and can help in understanding the accumulation of deformation fabrics in homogeneous and inhomogeneous flow, e.g. around boudi…
Sensitivity analysis of consumption cycles
2018
We study the special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional, non-invertible map with an additive stochastic component. Applying the concept of the stochastic sensitivity function and the related technique of confidence domains, we establish the conditions under which the system's complex consumption attractor is likely to become observable. It is shown that the level of noise intensities beyond which the complex consumption attractor is likely to be observed depends on the weight given to past consumption in an individual's preference adjustment.
Transitions in consumption behaviors in a peer-driven stochastic consumer network
2019
Abstract We study transition phenomena between attractors occurring in a stochastic network of two consumers. The consumption of each individual is strongly influenced by the past consumption of the other individual, while own consumption experience only plays a marginal role. From a formal point of view we are dealing with a special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional non-invertible map augmented by additive and/or parametric noise. In our investigation of the stochastic transitions we rely on a mixture of analytical and numerical techniques with a central role given to the concept of the stochastic sensitivity function and the related techni…
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.