Chaotic Firing Patterns Research Articles

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast–slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities (stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.). Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.

Pair of excitable FitzHugh-Nagumo elements: Synchronization, multistability, and chaos

We analyze a pair of excitable FitzHugh-Nagumo elements, each of which is coupled repulsively. While the rest state for each element is globally stable for a phase-attractive coupling, various firing patterns, including cyclic and chaotic firing patterns, exist in an phase-repulsive coupling region. Although the rest state becomes linearly unstable via a Hopf bifurcation, periodic solutions associated to the firing patterns is not connected to the Hopf bifurcation. This means that the solution branch emanating from the Hopf bifurcation is subcritical and unstable for any coupling strength. Various types of cyclic firing patterns emerge suddenly through saddle-node bifurcations. The parameter region in which different periodic solutions coexist is also found.

Relation between responsiveness to neurotransmitters and complexity of epileptiform activity in rat hippocampal CA1 neurons.

Our previous works suggested that sensitivity of neurons with chaotic firing patterns to stimuli is significantly greater than that in neurons with periodic firing patterns, which shows that responsiveness of neurons may depend on the complexity of the firing series. This study was performed to determine the relation between responsiveness of the hippocampal CA1 neurons with epileptiform activity (EA) to neurotransmitters and their complexity of firing series. Firing series of CA1 neurons were recorded extracellularly in rat hippocampal slice. Approximate entropy was used to describe the complexity of the interspike interval (ISI) series. EA was induced by local application of penicillin (1,000 IU/ml). The change of firing rate induced by neurotransmitters (glutamate and gamma-aminobutyric acid) was compared with that of the degree of complexity of ISI series in the process of EA. The excitatory responses to glutamate and the inhibitory responses to gamma-aminobutyric acid in CA1 neurons appeared to be decreased during the process of penicillin-induced EA. However, during this same process, the approximate entropy of the ISI series also was decreased significantly. The results suggest that the reduced responses to neurotransmitters of the CA1 neurons appear to be closely related to the onset of EA. Furthermore, these neurons show that the changes in responsiveness are closely parallel to the decrease of degree of complexity of firing series during penicillin epileptogenesis.

Period doubling of calcium spike firing in a model of a Purkinje cell dendrite.

Recordings from cerebellar Purkinje cell dendrites have revealed that in response to sustained current injection, the cell firing pattern can move from tonic firing of Ca(2+) spikes to doublet firing and even to quadruplet firing or more complex firing. These firing patterns are not modified substantially if Na(+) currents are blocked. We show that the experimental results can be viewed as a slow transition of the neuronal dynamics through a period-doubling bifurcation. To further support this conclusion and to understand the underlying mechanism that leads to doublet firing, we develop and study a simple, one-compartment model of Purkinje cell dendrite. The neuron can also exhibit quadruplet and chaotic firing patterns that are similar to the firing patterns that some of the Purkinje cells exhibit experimentally. The effects of parameters such as temperature, applied current, and potassium reversal potential in the model resemble their effects in experiments. The model dynamics involve three time scales. Ca(2+)- dependent K(+) currents, with intermediate time scales, are responsible for the appearance of doublet firing, whereas a very slow hyperpolarizing current transfers the neuron from tonic to doublet firing. We use the fast-slow analysis to separate the effects of the three time scales. Fast-slow analysis of the neuronal dynamics, with the activation variable of the very slow, hyperpolarizing current considered as a parameter, reveals that the transitions occurs via a cascade of period-doubling bifurcations of the fast and intermediate subsystem as this slow variable increases. We carry out another analysis, with the Ca(2+) concentration considered as a parameter, to investigate the conditions for the generation of doublet firing in systems with one effective variable with intermediate time scale, in which the rest state of the fast subsystem is terminated by a saddle-node bifurcation. We find that the scenario of period doubling in these systems can occur only if (1) the time scale of the intermediate variable (here, the decay rate of the calcium concentration) is slow enough in comparison with the interspike interval of the tonic firing at the transition but is not too slow and (2) there is a biostability of the fast subsystem of the spike-generating variables.

Lesion of the subthalamic nucleus or globus pallidus does not cause chaotic firing patterns in basal ganglia neurons in rats

The basal ganglia appears to play an important role in behavioral selection. One model (Berns and Sejnowski’s) of basal ganglia function argues that the subthalamic nucleus plays a critical role in this selection process and predicts that the subthalamic nucleus prevents the basal ganglia and its re-entrant circuits with the thalamus and cerebral cortex from developing chaotic oscillations. We tested this prediction by generating three-dimensional sequential interval state space plots of the spike trains from 684 globus pallidus, substantia nigra pars reticulata and subthalamic neurons recorded in intact, subthalamic lesioned and globus pallidus lesioned rats, neurons which had previously been analyzed with more standard statistical methods. Only 1 neuron (a globus pallidus neuron in a subthalamic lesioned rat) of the 684 showed a chaotic attractor. In no case did subthalamic nucleus lesion induce a chaotic firing pattern elsewhere in the basal ganglia.

Chaotic to periodic spontaneous pulsing in current driven silicon p-i-n structures

Abstract We report the experimental observations and modeling results confirming the transition to periodicity from chaotic (although still deterministic) spontaneous firing patterns for silicon p-i-n structures at 4.2K controlled by a constant current source. These patterns are determined by measuring the interpulse time interval (IPTI) between pulses. In contrast to a naive view, which suggests periodic patterns under current conservation, we see a rich spectrum of behavior due to the space charge effects, when the control parameter (drive current) is varied. In particular, a bi-modal pattern is found in which the IPTIs occur in two distinct groups rather than as a single continuous distribution. Nonlinear dynamics analysis tools as well as a statistical approach (i.e. Markov process) confirm the change from chaotic to periodic behavior as the control parameter increases. A theoretical model based on device physics for the buildup of space charge in the i-region of the diode giving insight into semiconductor device fabrication is developed to explain the bi-modal pulsing behavior observed. This can be used to enhance our understanding of various pulsing device applications, including IR detectors, parallel processors and neural networks.