Related papers: Periodic and chaotic dynamics in a map-based neuro…

The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…

Experimental records of active bundle motility are used to demonstrate the presence of a low-dimensional chaotic attractor in hair cell dynamics. Dimensionality tests from dynamic systems theory are applied to estimate the number of…

This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme…

We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore,…

We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…

Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…

A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations…

What is the reason for complex dynamical patterns registered from real biological neuronal networks? Noise and dynamical reconfiguring of a network (functional/dynamic connectome) were proposed as possible answers. In this case study, we…

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…

This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically…

Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…

In many complex systems, elementary units live in a chaotic environment and need to adapt their strategies to perform a task, by extracting information from the environment and controlling the feedback loop on it. One of the main example of…

We study the dynamics of one--dimensional discrete models of one--component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms of…

One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…

Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…

We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…

I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…

We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…