We investigate, both experimentally and theoretically, the period-doubling bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled with either smooth or border-collision dynamics. Using a modification of existing experimental techniques, we find a hybrid behavior: Very close to the bifurcation point, the dynamics is smooth, whereas further away it is border-collision-like. The essence of this behavior is captured by a model that exhibits what we call an unfolded border-collision bifurcation. This new model elucidates that, in an experiment, where only a limited number of data points can be measured, the smooth behavior of the bifurcation can easily be missed.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2447673 | PMC |
| http://dx.doi.org/10.1103/PhysRevLett.99.058101 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Investigation on the regular and chaotic dynamics of a ring network of five inertial Hopfield neural network: theoretical, analog and microcontroller simulation.
Cogn Neurodyn
December 2024
Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chittoor, India.
The studies conducted in this contribution are based on the analysis of the dynamics of a homogeneous network of five inertial neurons of the Hopfield type to which a unidirectional ring coupling topology is applied. The coupling is achieved by perturbing the next neuron's amplitude with a signal proportional to the previous one. The system consists of ten coupled ODEs, and the investigations carried out have allowed us to highlight several unusual and rarely related dynamics, hence the importance of emphasizing them.
View Article and Find Full Text PDFDynamic prediction of nonlinear waveform transitions in a thalamo-cortical neural network under a square sensory control.
Cogn Neurodyn
December 2024
School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi People's Republic of China.
Waveform transitions have high correlation to spike wave discharges and polyspike wave discharges in seizure dynamics. This research adopts nonlinear dynamics to study the waveform transitions in a cerebral thalamo-coritcal neural network subjected to a square sensory control via discretization and mappings. The continuous non-smooth network outputs are discretized to establish implicit mapping chains or loops for stable and unstable waveform solutions.
View Article and Find Full Text PDFShrimp structure as a test bed for ordinal pattern measures.
Chaos
December 2024
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany.
Identifying complex periodic windows surrounded by chaos in the two or higher dimensional parameter space of certain dynamical systems is a challenging task for time series analysis based on complex network approaches. This holds particularly true for the case of shrimp structures, where different bifurcations occur when crossing different domain boundaries. The corresponding dynamics often exhibit either period-doubling when crossing the inner boundaries or, respectively, intermittency for outer boundaries.
View Article and Find Full Text PDFMapping chaos: Bifurcation patterns and shrimp structures in the Ikeda map.
Chaos
December 2024
School of Electrical Engineering and Computer Science, College of Engineering & Mines, University of North Dakota, Grand Forks, North Dakota 58202-8367, USA.
This study examines the dynamical properties of the Ikeda map, with a focus on bifurcations and chaotic behavior. We investigate how variations in dissipation parameters influence the system, uncovering shrimp-shaped structures that represent intricate transitions between regular and chaotic dynamics. Key findings include the analysis of period-doubling bifurcations and the onset of chaos.
View Article and Find Full Text PDFChaotification and chaos control of q-homographic map.
Chaos
December 2024
Department of Mathematics, Indian Institute of Technology Jodhpur, 342030 Jodhpur, India.
This paper concerns the dynamical study of the q-deformed homographic map, namely, the q-homographic map, where q-deformation is introduced by Jagannathan and Sinha with the inspiration from Tsalli's q-exponential function. We analyze the q-homographic map by computing its basic nonlinear dynamics, bifurcation analysis, and topological entropy. We use the notion of a false derivative and the generalized Lambert W function of the rational type to estimate the upper bound on the number of fixed points of the q-homographic map.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!