Dmitry Sinelshchikov
Biography
Ikerbasque Research Fellow, Biofisika Institute (CSIC-UPV/EHU), Leioa, Spain
WEBSITE: https://www.biofisika.org/en/about/people/dmitry-sinelshchikov
Dmitry Sinelshchikov is an Ikerbasque Research Fellow at the Biofisika Institute (CSIC-UPV/EHU) (IBF) working in dynamical systems and ordinary differential equations with applications to biophysics, physics and medicine. Dmitry obtained his PhD in Mathematics and Physics (2010) from Moscow Engineering Physics Institute (MEPhI). After that Dmitry consequently worked from 2010 to 2019 as an Assistant Professor, Senior Lecturer and Associate Professor at MEPhI. During this period, his research was focused on analytical theory of differential equations and dynamical systems applied to fluid dynamics. Dmitry’s works on integrability of Li\'enard-type equations received recognition from the Russian Academy of Sciences and he was awarded the gold medal for young scientists in 2017. In 2019 Dmitry joined the HSE University as an Associate Professor, where he pursued his independent research line in integrability of dynamical systems and applied nonlinear dynamics. Since 2022 Dmitry is working in Spain at the IBF. In 2023 Dmitry was awarded simultaneously the Beatriz Galindo and Ikerbasque Research Fellow grants, of which he accepted the latter to continue working in biophysical applications of dynamical systems in a direct collaboration with experimental groups at the IBF.
Nonlinear dynamics in small groups of Hindmarsh-Rose neurons
In this talk we consider nonlinear dynamics in small groups of neurons that are described by the Hindmarsh-Rose model. This model aims to describe the bursting and spiking activity of membrane potential and its interactions with fast and slow ionic currents. While the Hindmarsh-Rose model for one neuron is well studied, the dynamics of coupled Hindmarsh-Rose neurons is still not completely understood. Here we study a model of three Hindmarsh – Rose neurons with directional electrical connections. We consider two fully-connected neurons that form a slave group which receives the signal from the master neuron via a directional coupling. We control the excitability of the neurons by setting the constant external currents. We study the possibility of excitation of the slave system in the stable resting state by the signal coming from the master neuron, to make it fire spikes/bursts tonically. We vary the coupling strength between the master and the slave systems as another control parameter. We calculate the borderlines of excitation by different types of signal in the control parameter space. We establish which of the resulting dynamical regimes are chaotic. We also demonstrate the possibility of excitation by a single burst or a spike in areas of control parameters, where the slave system is bistable. We calculate the borderlines of excitation by a single period of the excitatory signal.
