Browsing by Author "Klinshov, Vladimir"

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    Clustering promotes switching dynamics in networks of noisy neurons
    Franović, Igor; Klinshov, Vladimir
    Macroscopic variability is an emergent property of neural networks, typically manifested in spontaneous switching between the episodes of elevated neuronal activity and the quiescent episodes. We investigate the conditions that facilitate switching dynamics, focusing on the interplay between the different sources of noise and heterogeneity of the network topology. We consider clustered networks of rate-based neurons subjected to external and intrinsic noise and derive an effective model where the network dynamics is described by a set of coupled second-order stochastic mean-field systems representing each of the clusters. The model provides an insight into the different contributions to effective macroscopic noise and qualitatively indicates the parameter domains where switching dynamics may occur. By analyzing the mean-field model in the thermodynamic limit, we demonstrate that clustering promotes multistability, which gives rise to switching dynamics in a considerably wider parameter region compared to the case of a non-clustered network with sparse random connection topology.
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    Extending Dynamic Memory of Spiking Neuron Networks
    Klinshov, Vladimir; Kovalchuk, Andrey; Soloviev, Igor; Maslennikov, Oleg; Franović, Igor; Perc, Matjaž
    Explaining the mechanisms of dynamic memory, that allows for a temporary storage of information at the timescale of seconds despite the neuronal firing at the millisecond scale, is an important challenge not only for neuroscience, but also for computation in neuromorphic artificial networks. We demonstrate the potential origin of such longer timescales by comparing the spontaneous activity in excitatory neural networks with sparse random, regular and small-world connection topologies. We derive a mean-field model based on a self-consistent approach and white noise approximation to analyze the transient and long-term collective network dynamics. While the long-term dynamics is typically irregular and weakly correlated independent of the network architecture, especially long timescales are revealed for the transient activity comprised of switching fronts in regular and small-world networks with a small rewiring probability. Analyzing the dynamic memory of networks in performing a simple computational delay task within the framework of reservoir computing, we show that an optimal performance on average is reached for a regular connection topology if the input is appropriately structured, but certain instances of small-world networks may strongly deviate from configuration averages and outperform all the other considered network architectures.
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    Inverse stochastic resonance in a system of excitable active rotators with adaptive coupling
    Bačić, Iva; Klinshov, Vladimir; Nekorkin, Vladimir; Perc, Matjaž; Franović, Igor
    Inverse stochastic resonance is a phenomenon where an oscillating system influenced by noise exhibits a minimal oscillation frequency at an intermediate noise level. We demonstrate a novel generic scenario for such an effect in a multi-timescale system, considering an example of emergent oscillations in two adaptively coupled active rotators with excitable local dynamics. The impact of plasticity turns out to be twofold. First, at the level of multiscale dynamics, one finds a range of intermediate adaptivity rates that give rise to multistability between the limit cycle attractors and the stable equilibria, a condition necessary for the onset of the effect. Second, applying the fast-slow analysis, we show that the plasticity also plays a facilitatory role on a more subtle level, guiding the fast flow dynamics to parameter domains where the stable equilibria become focuses rather than nodes, which effectively enhances the influence of noise. The described scenario persists for different plasticity rules, underlying its robustness in the light of potential applications to neuroscience and other types of cell dynamics.
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    Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators
    Klinshov, Vladimir; Franović, Igor
    We consider the macroscopic regimes and the scenarios for the onset and the suppression of collective oscillations in a heterogeneous population of active rotators composed of excitable or oscillatory elements. We analyze the system in the continuum limit within the framework of Ott-Antonsen reduction method, determining the states with a constant mean field and their stability boundaries in terms of the characteristics of the rotators' frequency distribution. The system is established to display three macroscopic regimes, namely the homogeneous stationary state, where all the units lie at the resting state, the global oscillatory state, characterized by the partially synchronized local oscillations, and the heterogeneous stationary state, which includes a mixture of resting and asynchronously oscillating units. The transitions between the characteristic domains are found to involve a complex bifurcation structure, organized around three codimension-two bifurcation points: A Bogdanov-Takens point, a cusp point, and a fold-homoclinic point. Apart from the monostable domains, our study also reveals two domains admitting bistable behavior, manifested as coexistence between the two stationary solutions or between a stationary and a periodic solution. It is shown that the collective mode may emerge via two generic scenarios, guided by a saddle-node of infinite period or the Hopf bifurcation, such that the transition from the homogeneous to the heterogeneous stationary state under increasing diversity may follow the classical paradigm, but may also be hysteretic. We demonstrate that the basic bifurcation structure holds qualitatively in the presence of small noise or small coupling delay, with the boundaries of the characteristic domains shifted compared to the noiseless and the delay-free case.