Transient Periodicity in a Morris-Lecar Neural System | Zendy

Sreenivasan R. Nadar | Zendy; Vikas Rai | Zendy

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Transient Periodicity in a Morris-Lecar Neural System

Author(s) -

Sreenivasan R. Nadar,

Vikas Rai

Publication year - 2012

Publication title -

isrn biomathematics

Language(s) - English

Resource type - Journals

ISSN - 2090-7702

DOI - 10.5402/2012/546315

Subject(s) - transient (computer programming) , ordinary differential equation , excitatory postsynaptic potential , inhibitory postsynaptic potential , ode , chaotic , artificial neural network , oscillation (cell signaling) , dynamical systems theory , neural system , dynamical system (definition) , control theory (sociology) , physics , mathematics , neuroscience , biological system , computer science , differential equation , artificial intelligence , biology , mathematical analysis , genetics , control (management) , quantum mechanics , operating system

The dynamical complexity of a system of ordinary differential equations (ODEs) modeling the dynamics of a neuron that interacts with other neurons through on-off excitatory and inhibitory synapses in a neural system was investigated in detail. The model used Morris-Lecar (ML) equations with an additional autonomous variable representing the input from interaction of excitatory neuronal cells with local interneurons. Numerical simulations yielded a rich repertoire of dynamical behavior associated with this three-dimensional system, which included periodic, chaotic oscillation and rare bursts of episodic periodicity called the transient periodicity.

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