Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics
We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal
dynamics of high dimensional and reduced order complex systems using Reservoir …
dynamics of high dimensional and reduced order complex systems using Reservoir …
Border-Collision Bifurcations in
DJW Simpson - siam REVIEW, 2016 - SIAM
For piecewise-smooth maps, new dynamics can be created by varying parameters such that
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …
Complex dynamics of the simplest neuron model: Singular chaotic Shilnikov attractor as specific oscillatory neuron activity
NV Stankevich, AS Gonchenko, ES Popova… - Chaos, Solitons & …, 2023 - Elsevier
We study complex dynamics of the Chialvo model that is the simplest neuron-type model in
form of a four-parameter family of two-dimensional noninvertible maps (endomorphisms) …
form of a four-parameter family of two-dimensional noninvertible maps (endomorphisms) …
[图书][B] Chaotic modelling and simulation: analysis of chaotic models, attractors and forms
CH Skiadas, C Skiadas - 2008 - taylorfrancis.com
Offers Both Standard and Novel Approaches for the Modeling of SystemsExamines the
Interesting Behavior of Particular Classes of ModelsChaotic Modelling and Simulation …
Interesting Behavior of Particular Classes of ModelsChaotic Modelling and Simulation …
Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse
JP England, B Krauskopf, HM Osinga - SIAM Journal on Applied Dynamical …, 2004 - SIAM
We present an algorithm to compute the one-dimensional stable manifold of a saddle point
for a planar map. In contrast to current standard techniques, here it is not necessary to know …
for a planar map. In contrast to current standard techniques, here it is not necessary to know …
The dynamics of a triopoly Cournot game
This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic
demand and constant marginal costs, one of the rare cases where the reaction functions can …
demand and constant marginal costs, one of the rare cases where the reaction functions can …
A business cycle model with cubic nonlinearity
This paper deals with a simple multiplier-accelerator model of the business cycle, including
a cubic nonlinearity. The corresponding two dimensional iterative map is represented in …
a cubic nonlinearity. The corresponding two dimensional iterative map is represented in …
Global bifurcations of closed invariant curves in two-dimensional maps: a computer assisted study
In this paper we describe some sequences of global bifurcations involving attracting and
repelling closed invariant curves of two-dimensional maps that have a fixed point which may …
repelling closed invariant curves of two-dimensional maps that have a fixed point which may …
Complex patterns on the plane: different types of basin fractalization in a two-dimensional mapping
R López-Ruiz, D Fournier-Prunaret - International Journal of …, 2003 - World Scientific
Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic
maps are studied when the only parameter λ of the system is modified. Complex patterns on …
maps are studied when the only parameter λ of the system is modified. Complex patterns on …
Three-dimensional dissipative diffeomorphisms with homoclinic tangencies
JC Tatjer - Ergodic theory and Dynamical systems, 2001 - cambridge.org
Given a two-parameter family of three-dimensional diffeomorphisms\{f_ {a, b}\} _ {a, b}, with
a dissipative (but not sectionally dissipative) saddle fixed point, assume that a special type of …
a dissipative (but not sectionally dissipative) saddle fixed point, assume that a special type of …