Complex Response to Periodic Inhibition in Simple and Detailed Neuronal Models

1999 ◽  
Vol 11 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Corrado Bernasconi ◽  
Kaspar Schindler ◽  
Ruedi Stoop ◽  
Rodney Douglas
Keyword(s):  
Chaotic Behavior ◽  
Phase Locking ◽  
Neural Model ◽  
Realistic Model ◽  
Membrane Properties ◽  
Biophysical Model ◽  
Constant Current ◽  
Complex Response ◽  
Integrate And Fire ◽  
Neocortical Neurons

Constant current injection with superimposed periodic inhibition gives rise to phase locking as well as chaotic activity in rat neocortical neurons. Here we compare the behavior of a leaky integrate-and-fire neural model with that of a biophysically realistic model of the rat neuron to determine which membrane properties influence the response to such stimuli. We find that only the biophysical model with voltage-sensitive conductances can produce chaotic behavior.

scholarly journals Interspike Interval Correlations, Memory, Adaptation, and Refractoriness in a Leaky Integrate-and-Fire Model with Threshold Fatigue

2003 ◽  
Vol 15 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Maurice J. Chacron ◽  
Khashayar Pakdaman ◽  
André Longtin
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Discharge Rate ◽  
Correlation Coefficients ◽  
Stimulus Onset ◽  
Constant Current ◽  
Integrate And Fire ◽  
Sinusoidal Currents ◽  
Lif Neuron ◽  
Sensitivity To Initial Conditions

Neuronal adaptation as well as interdischarge interval correlations have been shown to be functionally important properties of physiological neurons. We explore the dynamics of a modified leaky integrate-and-fire (LIF) neuron, referred to as the LIF with threshold fatigue, and show that it reproduces these properties. In this model, the postdischarge threshold reset depends on the preceding sequence of discharge times. We show that in response to various classes of stimuli, namely, constant currents, step currents, white gaussian noise, and sinusoidal currents, the model exhibits new behavior compared with the standard LIF neuron. More precisely, (1) step currents lead to adaptation, that is, a progressive decrease of the discharge rate following the stimulus onset, while in the standard LIF, no such patterns are possible; (2) a saturation in the firing rate occurs in certain regimes, a behavior not seen in the LIF neuron; (3) interspike intervals of the noise-driven modified LIF under constant current are correlated in a way reminiscent of experimental observations, while those of the standard LIF are independent of one another; (4) the magnitude of the correlation coefficients decreases as a function of noise intensity; and (5) the dynamics of the sinusoidally forced modified LIF are described by iterates of an annulus map, an extension to the circle map dynamics displayed by the LIF model. Under certain conditions, this map can give rise to sensitivity to initial conditions and thus chaotic behavior.

Spike-Timing-Dependent Hebbian Plasticity as Temporal Difference Learning

2001 ◽  
Vol 13 (10) ◽  
pp. 2221-2237 ◽  
Author(s):  
Rajesh P. N. Rao ◽  
Terrence J. Sejnowski
Keyword(s):  
Cortical Neuron ◽  
Action Potentials ◽  
Learning Rule ◽  
Spike Timing ◽  
Biophysical Model ◽  
Excitatory Synapses ◽  
Temporal Difference ◽  
Temporal Difference Learning ◽  
Neocortical Neurons ◽  
Hebbian Plasticity

A spike-timing-dependent Hebbian mechanism governs the plasticity of recurrent excitatory synapses in the neocortex: synapses that are activated a few milliseconds before a postsynaptic spike are potentiated, while those that are activated a few milliseconds after are depressed. We show that such a mechanism can implement a form of temporal difference learning for prediction of input sequences. Using a biophysical model of a cortical neuron, we show that a temporal difference rule used in conjunction with dendritic backpropagating action potentials reproduces the temporally asymmetric window of Hebbian plasticity observed physiologically. Furthermore, the size and shape of the window vary with the distance of the synapse from the soma. Using a simple example, we show how a spike-timing-based temporal difference learning rule can allow a network of neocortical neurons to predict an input a few milliseconds before the input's expected arrival.

An Electrochemical Model Based Optimal Charging Algorithm for Lithium-Ion Batteries

2015 ◽  
Author(s):  
Sourav Pramanik ◽  
Sohel Anwar
Keyword(s):  
Management System ◽  
Optimization Problems ◽  
Optimal Algorithm ◽  
Algorithm Design ◽  
Lithium Ion ◽  
Cell Voltage ◽  
Realistic Model ◽  
Constant Current ◽  
Battery Management System ◽  
Model Based

In recent years, Lithium-Ion battery has gathered lot of importance in many forms of energy storage applications due to its overwhelming benefits. Any battery pack alone cannot achieve its optimal performance unless there is a robust and efficient energy management system, commonly known as battery management system or BMS. The Lithium-Ion charger is a voltage-limiting device that is similar to the lead acid system. The difference lies in a higher cell voltage; tighter voltage tolerance and the absence of trickle or float charge at full charge. In this work, we propose the design of a novel optimal strategy for charging the battery that better suits the battery performance. A performance index is defined that aims at minimizing the effort of regeneration along with a minimum deviation from the rated maximum thresholds for cell temperature and charging current. A more realistic model based on battery electrochemistry is used for the optimal algorithm design as opposed to equivalent circuit models. To solve the optimization problem, Pontryagin’s principle is used which is very effective for constrained optimization problems with both state and input constraints. Simulation results show that the proposed optimal charging algorithm is capable of shortening the charging time of a Lithium Ion cell while maintaining the temperature constraint when compared with the standard constant current charging.

Neural repetitive firing: a comparative study of membrane properties of crustacean walking leg axons

1975 ◽  
Vol 38 (4) ◽  
pp. 922-932 ◽  
Author(s):  
J. A. Connor
Keyword(s):  
Membrane Conductance ◽  
Firing Frequency ◽  
Membrane Properties ◽  
Constant Current ◽  
Repetitive Firing ◽  
Type I ◽  
Frequency Range ◽  
Type Iii ◽  
Range Type ◽  
Sucrose Gap

1. Repetitive activity and membrane conductance parameters of crab walking leg axons have been studied in the double sucrose gap. 2. The responses to constant current stimulus could be classified into three catagories; highly repetitive with wide firing frequency range, type I; highly repetitive with narrow frequency range, type II; and nonrepetitive or repetitive to only a limited degree, type III. The minimum firing frequency for type I axons was much greater than for other recording techniques. 3. Voltage-clamp currents in type III axons were qualitatively similar to those of squid or lobster axon. 4. The outward membrane currents of type I and II axons showed a transient phase in addition to the usual delayed current. The magnitude of this transient was a function of both the holding and test voltages. 5. The direction of the transient current reversed in potassium-rich saline. 6. The type I repetitive response in the walking leg axons appears to be generated by the same types of conductance changes that have been demonstrated in molluscan central neurons.

Volterra Equations with Periodic Nonlinearities: Multistability, Oscillations and Cycle Slipping

2019 ◽  
Vol 29 (05) ◽  
pp. 1950068 ◽  
Author(s):  
Vera B. Smirnova ◽  
Anton V. Proskurnikov
Keyword(s):  
Frequency Domain ◽  
Chaotic Behavior ◽  
Linear Time ◽  
Phase Locking ◽  
Limit Equilibrium ◽  
A Priori ◽  
Phase Locked Loops ◽  
Volterra Equations ◽  
Convergence Criterion ◽  
Quadratic Constraints

In this paper, systems of nonlinear integro-differential Volterra equations are examined that can be represented as feedback interconnections of linear time-invariant block and periodic nonlinearities. The interest in such systems is motivated by their numerous applications in mechanical, electrical and communication engineering; examples include, but are not limited to, models of phase-locked loops, pendulum-like mechanical systems, coupled vibrational units and electric machines. Systems with periodic nonlinearities are usually featured by multistability and have infinite sequences of (locally) stable and unstable equilibria; their trajectories may exhibit nontrivial (e.g. chaotic) behavior. We offer frequency-domain criteria, ensuring convergence of any solution to one of the equilibria points, and this property is referred to as the gradient-like behavior and corresponds to phase locking in synchronization systems. Although it is hard to find explicitly the equilibrium, attracting a given trajectory, we give a constructive estimate for the distance between this limit equilibrium and the initial condition. The relevant estimates are closely related to the analysis of cycle slipping in synchronization systems. In the case where the criterion of gradient-type behavior fails, a natural question arises — which nonconverging solutions may exist in the system and, in particular, how many periodic solutions it has. We show that a relaxation of the frequency-domain convergence criterion ensures the absence of high-frequency periodic orbits. The results obtained in the paper are based on the method of integral quadratic constraints that has arisen in absolute stability theory and stems from Popov’s techniques of “a priori integral indices”. We illustrate the analytic results by numerical simulations.

Electrophysiological properties of neurons in guinea pig bronchial parasympathetic ganglia

1990 ◽  
Vol 259 (6) ◽  
pp. L403-L409 ◽  
Author(s):  
A. C. Myers ◽  
B. J. Undem ◽  
D. Weinreich
Keyword(s):  
Guinea Pig ◽  
Vagus Nerve ◽  
Action Potentials ◽  
Receptor Activation ◽  
Membrane Properties ◽  
Constant Current ◽  
Parasympathetic Ganglia ◽  
Stimulation Of ◽  
Passive Membrane

Active and passive membrane membrane properties of parasympathetic neurons were examined in vitro in a newly localized ganglion on the right bronchus of the guinea pig. Neurons could be classified as “tonic” or “phasic” based on their action potential discharge response to suprathreshold depolarizing constant current steps. Tonic neurons (39%) responded with repetitive action potentials sustained throughout the current step, whereas phasic neurons (61%) responded with an initial burst of action potentials at the onset of the step but then accommodated. Tonic and phasic neurons could not be differentiated by other active or passive membrane properties. Electrical stimulation of the vagus nerve elicited one to three temporally distinct fast nicotinic excitatory potentials, and tetanic stimulation of the vagus nerve evoked slow depolarizing (10% of neurons) and hyperpolarizing (25% of neurons) potentials; the latter was mimicked by muscarinic receptor activation. Similar slow and fast postsynaptic potentials were observed in both tonic and phasic neurons. We suggest neurons within the bronchial ganglion possess membrane and synaptic properties capable of integrating presynaptic stimuli.

Sign in / Sign up

Export Citation Format

Share Document