Biomedical subjects

E M Izhikevich

Publications and source records attributed to E M Izhikevich.

5 recordsLinked to original sources

PubMed1996

Synaptic organizations and dynamical properties of weakly connected neural oscillators. I. Analysis of a canonical model.

We study weakly connected networks of neural oscillators near multiple Andronov-Hopf bifurcation points. We analyze relationships between synaptic organizations (anatomy) of the networks and their dynamical properties (function). Our principal assumptions are: (1) Each neural oscillator comprises two populations of neurons; excitatory and inhibitory ones; (2) activity of each population of neurons is described by a scalar (one-dimensional) variable; (3) each neural oscillator is near a nondegenerate supercritical Andronov-Hopf bifurcation point; (4) the synaptic connections between the neural oscillators are weak. All neural networks satisfying these hypotheses are governed by the same dynamical system, which we call the canonical model. Studying the canonical model shows that: (1) A neural oscillator can communicate only with those oscillators which have roughly the same natural frequency. That is, synaptic connections between a pair of oscillators having different natural frequencies are functionally insignificant. (2) Two neural oscillators having the same natural frequencies might not communicate if the connections between them are from among a class of pathological synaptic configurations. In both cases the anatomical presence of synaptic connections between neural oscillators does not necessarily guarantee that the connections are functionally significant. (3) There can be substantial phase differences (time delays) between the neural oscillators, which result from the synaptic organization of the network, not from the transmission delays. Using the canonical model we can illustrate self-ignition and autonomous quiescence (oscillator death) phenomena. That is, a network of passive elements can exhibit active properties and vice versa. We also study how Dale's principle affects dynamics of the networks, in particular, the phase differences that the network can reproduce. We present a complete classification of all possible synaptic organizations from this point of view. The theory developed here casts some light on relations between synaptic organization and functional properties of oscillatory networks. The major advantage of our approach is that we obtain results about all networks of neural oscillators, including the real brain. The major drawback is that our findings are valid only when the brain operates near a critical regime, viz. for a multiple Andronov-Hopf bifurcation.

Cell Death↗

PubMed1996

Synaptic organizations and dynamical properties of weakly connected neural oscillators. II. Learning phase information.

This is the second of two articles devoted to analyzing the relationship between synaptic organizations (anatomy) and dynamical properties (function) of networks of neural oscillators near multiple supercritical Andronov-Hopf bifurcation points. Here we analyze learning processes in such networks. Regarding learning dynamics, we assume (1) learning is local (i.e. synaptic modification depends on pre- and postsynaptic neurons but not on others), (2) synapses modify slowly relative to characteristic neuron response times, (3) in the absence of either pre- or postsynaptic activity, the synapse weakens (forgets). Our major goal is to analyze all synaptic organizations of oscillatory neural networks that can memorize and retrieve phase information or time delays. We show that such network have the following attributes: (1) the rate of synaptic plasticity connected with learning is determined locally by the presynaptic neurons, (2) the excitatory neurons must be long-axon relay neurons capable of forming distant connections with other excitatory and inhibitory neurons, (3) if inhibitory neurons have long axons, then the network can learn, passively forget and actively unlearn information by adjusting synaptic plasticity rates.

Learning↗

PubMed1991

Memory, learning and neuromediators.

We consider a model of a neural network where the individual cells interact only by releasing and absorbing the molecules of a neuromediator. We show that such a system can realize the function of associative memory. A learning mechanism based on the chemotaxis is proposed and numerically investigated.

Association Learning↗

PubMedDate not supplied

Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use FM radio principles?

We consider all models of the thalamo-cortical system that satisfy the following two assumptions: (1) each cortical column is an autonomous oscillator; (2) connections between cortical columns and the thalamus are weak. Our goal is to deduce from these assumptions general principles of thalamo-cortical interactions that are independent of the equations describing the system. We find that the existence of synaptic connections between any two cortical columns does not guarantee that the columns interact: They interact only when there is a certain nearly resonant relation between their frequencies, which implies that the interactions are frequency modulated (FM). When the resonance relation holds, the cortical columns interact through phase modulations. Thus, communications between weakly connected cortical oscillators employ a principle similar to that in FM radio: The frequency of oscillation encodes the channel of communication, while the information is transmitted via phase modulations. If the thalamic input has an appropriate frequency, then it can dynamically link any two cortical columns, even those that have non-resonant frequencies and would otherwise be unlinked. Thus, by adjusting its temporal activity, the thalamus has control over information processing taking place in the cortex. Our results suggest that the mean firing rate (frequency) of periodically spiking neuron does not carry any information other than identifying a channel of communication. Information (i.e. neural code) is carried through modulations of interspike intervals.

Cerebral Cortex↗

PubMedDate not supplied

Resonate-and-fire neurons.

We suggest a simple spiking model-resonate-and-fire neuron, which is similar to the integrate-and-fire neuron except that the state variable is complex. The model provides geometric illustrations to many interesting phenomena occurring in biological neurons having subthreshold damped oscillations of membrane potential. For example, such neurons prefer a certain resonant frequency of the input that is nearly equal to their eigenfrequency, they can be excited or inhibited by a doublet (two pulses) depending on its interspike interval, and they can fire in response to an inhibitory input. All these properties could be observed in Hodgkin-Huxley-type models. We use the resonate-and-fire model to illustrate possible sensitivity of biological neurons to the fine temporal structure of the input spike train. Being an analogue of the integrate-and-fire model, the resonate-and-fire model is computationally efficient and suitable for simulations of large networks of spiking neurons.

Action Potentials↗