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- ItemDynamics of a stochastic excitable system with slowly adapting feedback(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Franović, Igor; Yanchuk, Serhiy; Eydam, Sebastian; Bačić, Iva; Wolfrum, MatthiasWe study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance, or effectively control the features of the stochastic bursting. The setup can be considered as a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker-Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.
- ItemNoise-induced switching in two adaptively coupled excitable systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Bačić, Iva; Yanchuk, Serhiy; Wolfrum, Matthias; Franović, IgorWe demonstrate that the interplay of noise and plasticity gives rise to slow stochastic fluctuations in a system of two adaptively coupled active rotators with excitable local dynamics. Depending on the adaptation rate, two qualitatively different types of switching behavior are observed. For slower adaptation, one finds alternation between two modes of noise-induced oscillations, whereby the modes are distinguished by the different order of spiking between the units. In case of faster adaptation, the system switches between the metastable states derived from coexisting attractors of the corresponding deterministic system, whereby the phases exhibit a bursting-like behavior. The qualitative features of the switching dynamics are analyzed within the framework of fast-slow analysis.