Examinando por Autor "Bashkirtseva, Irina"

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Noise-induced complex dynamics and synchronization in the map-based Chialvo neuron model
(Elsevier, 2023-01) Bashkirtseva, Irina; Ryashko, Lev; Used, Javier; Seoane, Jesús M.; Fernández Sanjuán, Miguel Ángel
The paper considers a stochastic version of the conceptual map-based Chialvo model of neural activity. Firstly, we focus on the parametric zone where this model exhibits monoand bistability with coexistence of equilibria and oscillatory spiking attractors forming closed invariant curves. Stochastic effects of excitement and generation of bursting are studied both numerically and analytically by confidence ellipses. A phenomenon of the noise-induced transition to chaos in a localized two-parametric zone is discussed. Besides, we also study the phenomenon of synchronization between neurons by using a two-neuron network with a small coupling. In this scenario, we have found critical values of noise for which we obtain a good performance for the synchronization between the neurons of the network.
The role of noise in the tumor dynamics under chemotherapy treatment
(Springer, 2021) Bashkirtseva, Irina; Ryashko, Lev; Duarte, Jorge; Seoane, Jesús M.; Sanjuán, Miguel A. F.
Dynamical systems modeling tumor growth have been investigated to analyze the dynamics between tumor and healthy cells. Recent theoretical studies indicate that these interactions may lead to different dynamical outcomes under the effect of particular cancer therapies. In the present paper, we derive a system of nonlinear differential equations, in order to investigate solid tumors in vivo, taking into account the impact of chemotherapy on both tumor and healthy cells. We start by studying our model only in terms of deterministic dynamics under the variation of a drug concentration parameter. Later, with the introduction of noise, a stochastic model is used to analyze the impact of the unavoidable random fluctuations. As a result, new insights into noise-induced transitions are provided and illustrated in detail using techniques from dynamical systems and from the theory of stochastic processes.