Modeling of spiking-bursting neural behavior using two-dimensional map

Abstract

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons. PACS number(s): 05.45.+b, 87.22.-q

Self-organization in the olfactory system: one shot odor recognition in insects

“…Our model is implemented with spiking neurons represented by a phenomenological, discrete time dynamical map [4,38] with fixed time steps ∆t = 0.5ms. In contrast to phenomenological conductance based models, this map can be computed very quickly such that we can simulate neural ensembles with realistic population sizes, on the order of thousands of neurons.…”

“…We used the original map neurons [38] that match this generic and well-tested Hodgkin-Huxley model for spiking neurons instead of developing a custom model to match the emerging line of models for the honeybee KCs [20,34,54]. While the current study is closer to the biological systems than our previous work [19], it is not yet describing a specific insect and specializing to a neuron model designed to match honeybee KCs would be pretentious.…”

Coherence resonance in models of an excitable neuron with noise in both the fast and slow dynamics

“…We first consider a discrete-time (iterated map) model [25] whose behavior mimics that of physiological neurons [26,27]. The model has two dynamical variables: one corresponding to the membrane voltage in a neuron and the other to a gating-ion concentration (usually Ca 2+ in actual neurons).…”

Biomimetic approaches to the control of underwater walking machines

“…In particular, neuronal network-based controllers allow flexibility and robustness unavailable to deterministic programs (Abarbanel & Rabinovich 2001). We have been evaluating two different types of neuronal-based controllers for application to the lobster robot, ENs (Pinto et al 2000) and discrete time map-based neurons (Rulkov 2002). UCSD ENs are based on a dynamical model of lobster neurons formalized by the Hindmarsh & Rose (1984) equations.…”

“…Second, these reflexes are going to require a lot of annealing; hence there is a need for interactive programming. Discrete time map-based neurons provide an attractive alternative for implementation of the complex circuitry necessary for the control of adaptive behaviour by a robotic brain (Rulkov 2002). The map-based neurons are available for rapid prototyping in the LABVIEW (National Instruments, Austin, TX) environment 3 .…”