Conductance-based (CB) models are a class of high dimensional dynamical systems derived from biophysical principles to describe in detail the electrical dynamics of single neurons. Despite the high dimensionality of these models, the dynamics observed for realistic parameter values is generically planar and can be minimally described by two equations. In this work, we derive the conditions to h...

In recent years there has been an increased interest in working with piece-wise linear caricatures of nonlinear models. Such models are often preferred over more detailed conductance based models for their small number of parameters and low computational overhead. Moreover, their piece-wise linear (PWL) form, allow the construction of action potential shapes in closed form as well as the calcul...

Bursting is a complex multiple-time-scale nonlinear phenomenon in nervous system and exhibits diverse patterns, which modulated by the excitatory or inhibitory effect to achieve physiological functions. According bifurcations of fast subsystem, bursting classified as different patterns including mixed-mode bursting. Recently, many studies have found paradoxical phenomena contrary common concept...

We study synchronization transitions and pattern formation on small-world networks consisting of Morris–Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays c...

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and ...

Abstract: Pyramidal neurons in the intact brain are bombarded by synaptic inputs that cause tonic depolarization, shunting, and noisy fluctuations in membrane potential; by comparison, pyramidal neurons in acute slices experience little background input. Such differences in operating conditions can compromise extrapolation of in vitro data to explain neuronal operation in vivo. For instance, py...

The response of a neural cell to an external stimulus can follow one of two patterns: nonresonant neurons monotonically relax to the resting state after excitation while resonant ones show subthreshold oscillations. We investigate how these subthreshold properties of neurons affect their suprathreshold response. Conversely we ask the following: Can we distinguish between both types of neuronal ...

Periodic bursting behavior in neurons is a recurrent transition between a quiescent state and repetitive spiking. When the transition to repetitive spiking occurs via a subcritical Andronov–Hopf bifurcation and the transition to the quiescent state occurs via fold limit cycle bifurcation, the burster is said to be of elliptic type (also known as a “subHopf/fold cycle” burster). Here we study th...

During normal aging, quite a lot of age-related changes happen like short-term memory, shakiness and muscle weakness occurring in human beings, and further affect the brain function, such as the altered calcium influx through the calcium ion channels, neural plasticity deficits, and other neurodegenerative processes. Some of them will even develop to a fatal neurodegenerative disorder like Alzh...

We present a novel approach to quantify the statistical interdependence of two time series, referred to as stochastic event synchrony (SES). The first step is to extract the two given time series. The next step is to try to align events from one time series with events from the other. The better the alignment the more similar the two series are considered to be. More precisely, the similarity i...