ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Phenomenon of the van der pol equation

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters.
• The biography of van der Pol, history of his equation and supposed precursors.

Feature of simultaneous influence of excitatory synaptic currents on a neuron with differential responses

The simultaneous influence of excitatory synaptic stimuli (the tonic AMPA and NMDA currents) on the neuron model with response differentiation is studied. It is shown that different types of neuron activity (rest state, low frequency or high frequency firing) are observed depending on the conductance of the AMPA and NMDA receptors. It is found that for the certain parameters values if both types of receptors are activated simultaneously, it is possible to obtain maximal frequency to be approximately 20% greater than that with the NMDA current alone.

The impact of electrical couplings on the dynamics of the ensemble of inhibitory coupled neuron-like elements

Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator. Aim of work is to study of influence of coupling strength and frequency detuning between elements in the case of regime of sequential activity that is observed in ensemble of neuronlike elements with chemical inhibitory couplings. Method. The research is made with usage of analytical methods of nonlinear dynamics and computer modeling. Results.