ArticleCognitive neurodynamics2012
Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns.
Article in Cognitive neurodynamics, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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17 citing papers in PubMed.
- Limitations of Variational Laplace-Based Dynamic Causal Modelling for Multistable Cortical Circuits.Neuroinformatics · 2026Article
- Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model.Cognitive neurodynamics · 2024Article
- Learning-based sliding mode synchronization for fractional-order Hindmarsh-Rose neuronal models with deterministic learning.Frontiers in neuroscience · 2023Article
- Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system.Cognitive neurodynamics · 2022Article
- Emergent Bioanalogous Properties of Blockchain-based Distributed Systems.Origins of life and evolution of the biosphere : the journal of the International Society for the Study of the Origin of Life · 2021Article
- Research on cascading high-dimensional isomorphic chaotic maps.Cognitive neurodynamics · 2021Article
- Bursting in cerebellar stellate cells induced by pharmacological agents: Non-sequential spike adding.PLoS computational biology · 2020Article
- Computational study on neuronal activities arising in the pre-Bötzinger complex.Cognitive neurodynamics · 2017Article
- Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations.BMC systems biology · 2017Article
- A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space.Cognitive neurodynamics · 2017Article
- Dynamics of in-phase and anti-phase bursting in the coupled pre-Bötzinger complex cells.Cognitive neurodynamics · 2017Article
- Chaos and Hyperchaos in a Model of Ribosome Autocatalytic Synthesis.Scientific reports · 2016Article
- Presence of a Chaotic Region at the Sleep-Wake Transition in a Simplified Thalamocortical Circuit Model.Frontiers in computational neuroscience · 2016Article
- Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors.Frontiers in computational neuroscience · 2015Article
- Period doubling induced by thermal noise amplification in genetic circuits.Scientific reports · 2014Article
- Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays.Cognitive neurodynamics · 2013Article
- Biological experimental observations of an unnoticed chaos as simulated by the Hindmarsh-Rose model.PloS one · 2013Article
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4 authors.
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Abstract
Period-doubling bifurcation to chaos were discovered in spontaneous firings of Onchidium pacemaker neurons. In this paper, we provide three cases of bifurcation processes related to period-doubling bifurcation cascades to chaos observed in the spontaneous firing patterns recorded from an injured site of rat sciatic nerve as a pacemaker. Period-doubling bifurcation cascades to period-4 (π(2,2)) firstly, and then to chaos, at last to a periodicity, which can be period-5, period-4 (π(4)) and period-3, respectively, in different pacemakers. The three bifurcation processes are labeled as case I, II and III, respectively, manifesting procedures different to those of period-adding bifurcation. Higher-dimensional unstable periodic orbits (UPOs) can be detected in the chaos, built close relationships to the periodic firing patterns. Case III bifurcation process is similar to that discovered in the Onchidium pacemaker neurons and simulated in theoretical model-Chay model. The extra-large Feigenbaum constant manifesting in the period-doubling bifurcation process, induced by quasi-discontinuous characteristics exhibited in the first return maps of both ISI series and slow variable of Chay model, shows that higher-dimensional periodic behaviors appeared difficult within the period-doubling bifurcation cascades. The results not only provide examples of period-doubling bifurcation to chaos and chaos with higher-dimensional UPOs, but also reveal the dynamical features of the period-doubling bifurcation cascades to chaos.
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