Andrey Shilnikov - Academia.edu (original) (raw)
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Papers by Andrey Shilnikov
International Journal of Bifurcation and Chaos, 2014
International Journal of Bifurcation and Chaos, 2015
Physica D: Nonlinear Phenomena, 2011
Nonlinear Systems and Complexity, 2015
World Scientific Series on Nonlinear Science Series A, 1998
World Scientific Series on Nonlinear Science Series A, 1998
World Scientific Series on Nonlinear Science Series A, 1998
Regular and Chaotic Dynamics, 2014
World Scientific Series on Nonlinear Science Series A, 2001
International Journal of Bifurcation and Chaos, 2014
Journal of neurophysiology, Jan 14, 2015
Ionic concentrations fluctuate significantly during epileptic seizures. In this study, we demonst... more Ionic concentrations fluctuate significantly during epileptic seizures. In this study, we demonstrate that changes in the K(+) and Na(+) intra- and extracellular ion concentrations during seizure affect the neuron membrane potential by modulating the outward Na(+)/K(+) pump current. First, we show that increase of the outward Na(+)/K(+) pump current mediates termination of seizures when there is a progressive increase in the intracellular Na(+) concentration. Second, we show that the Na(+)/K(+) pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na(+)/K(+) pump. Overall, our study demonstrates the profound role of the current mediated by Na(+)/K(+) on the stability of neuronal dynamics that was previously unknown.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of mu... more Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and o...
Physical review letters, Jan 4, 2005
We study a continuous and reversible transition between periodic tonic spiking and bursting activ... more We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square root alpha-alpha0 as the transition value alpha0 is approached.
International Journal of Bifurcation and Chaos, 2014
International Journal of Bifurcation and Chaos, 2014
International Journal of Bifurcation and Chaos, 2015
Physica D: Nonlinear Phenomena, 2011
Nonlinear Systems and Complexity, 2015
World Scientific Series on Nonlinear Science Series A, 1998
World Scientific Series on Nonlinear Science Series A, 1998
World Scientific Series on Nonlinear Science Series A, 1998
Regular and Chaotic Dynamics, 2014
World Scientific Series on Nonlinear Science Series A, 2001
International Journal of Bifurcation and Chaos, 2014
Journal of neurophysiology, Jan 14, 2015
Ionic concentrations fluctuate significantly during epileptic seizures. In this study, we demonst... more Ionic concentrations fluctuate significantly during epileptic seizures. In this study, we demonstrate that changes in the K(+) and Na(+) intra- and extracellular ion concentrations during seizure affect the neuron membrane potential by modulating the outward Na(+)/K(+) pump current. First, we show that increase of the outward Na(+)/K(+) pump current mediates termination of seizures when there is a progressive increase in the intracellular Na(+) concentration. Second, we show that the Na(+)/K(+) pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na(+)/K(+) pump. Overall, our study demonstrates the profound role of the current mediated by Na(+)/K(+) on the stability of neuronal dynamics that was previously unknown.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of mu... more Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and o...
Physical review letters, Jan 4, 2005
We study a continuous and reversible transition between periodic tonic spiking and bursting activ... more We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square root alpha-alpha0 as the transition value alpha0 is approached.
International Journal of Bifurcation and Chaos, 2014