100 citations · 377 across the 14 of their papers we have counts for
14 papers
Adaptation rules inducing synchronization of heterogeneous Kuramoto oscillator network with triadic couplings
Anastasiia Emelianova, Vladimir Nekorkin
A class of adaptation functions is found for which a synchronous oscillation mode exists in the network of phase oscillators with triadic couplings. It is shown that the destructio…
Hierarchical frequency clusters in adaptive networks of phase oscillators
Rico Berner, Jan Fialkowski, Dmitry Kasatkin +3
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system o…
Itinerant chimeras in an adaptive network of pulse-coupled oscillators
Dmitry Kasatkin, Vladimir Klinshov, Vladimir Nekorkin
In a network of pulse-coupled oscillators with adaptive coupling, we a dynamical regime which we call an `itinerant chimera'. Similarly as in classical chimera states, the network…
Embedding the dynamics of a single delay system into a feed-forward ring
Vladimir Klinshov, Dmitry Shchapin, Serhiy Yanchuk +3
We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its ne…
Phase response function for oscillators with strong forcing or coupling
Vladimir Klinshov, Serhiy Yanchuk, Artur Stephan +1
Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework fo…
Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons
Oleg V. Maslennikov, Dmitry S. Shchapin, Vladimir I. Nekorkin
We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network…
Mean-field dynamics of a population of stochastic map neurons
Igor Franovic, Oleg V. Maslennikov, Iva Bacic +1
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant…
Phase response curves for models of earthquake fault dynamics
Igor Franović, Srđan Kostić, Matjaz Perc +3
We systematically study effects of external perturbations on models describing earthquake fault dynamics. The latter are based on the framework of the Burridge-Knopoff spring-block…
Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback
Vladimir Klinshov, Leonhard Luecken, Dmitry Shchapin +2
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscilla…
Stability threshold approach for complex dynamical systems
Vladimir V. Klinshov, Vladimir I. Nekorkin, Jürgen Kurths
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weake…
Multistable jittering in oscillators with pulsatile delayed feedback
Vladimir Klinshov, Leonhard Lücken, Dmitry Shchapin +2
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such syste…
Evolving dynamical networks with transient cluster activity
Oleg V. Maslennikov, Vladimir I. Nekorkin
We study transient sequential dynamics of evolving dynamical networks, i.e., those having active nodes and links and activity-dependent topology. We show that such networks can gen…
Chaotic oscillations in a map-based model of neural activity
Maurice Courbage, V. I. Nekorkin, L. V. Vdovin
We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find c…
Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons
M. Courbage, V. Kazentsev, V. I. Nekorkin +1
The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron mode…