Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well n...

The crab Cancer borealis undergoes large daily fluctuations in environmental temperature (8-24°C) and must maintain appropriate neural function in the face of this perturbation. In the pyloric circuit of the crab stomatogastric ganglion, we pharmacologically isolated the pacemaker kernel (the AB and PD neurons) and characterized its behavior in response to temperature ramps from 7°C to 31°C. Fo...

We introduce three- and two-dimensional biophysical models of cardiac excitability derived from a 14-dimensional model of the sinus venosus [Rasmusson, R., et al., 1990. Am. J. Physiol. 259, H352-369]. The reduced models capture normal pacemaking dynamics with a small complement of ionic currents. The two-dimensional model bears some similarities with the Morris-Lecar model [Morris, C., Lecar, ...

We undertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli. Recalling and extending results from the literature, we compute phase response curves (PRCs) valid near bifurcations to periodic firing for Hindmarsh-Rose, Hodgkin-Huxley, FitzHugh-Nagumo, and Morris-Lecar models, encompassing the four generic (codimension one) bifurcatio...

We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space R ×E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rate...

 The use of optimal orthogonal array latin hypercube designs is proposed. Orthogonal arrays were proposed for constructing latin hypercube designs by Tang (1993). Such designs generally have better space filling properties than random latin hypercube designs. Even so, these designs do not necessarily fill the space particularly well. As a result, we consider orthogonal-array-based latin...

The behavior of a system of coupled ordinary differential equations is studied in order to characterize the CA3 region of the hippocampus. Clustering and synchronization behavior in a one-dimensional array of cells modeled by a modified Morris–Lecar model is analyzed in terms of a time delay included in the model. The random formation of phase dislocations whose number increases with the time d...

Using an exactly solvable cortical model of a neuronal network, we show that, by increasing the intensity of shot noise (flow of random spikes bombarding neurons), the network undergoes first-and second-order non-equilibrium phase transitions. We study the nature of the transitions, bursts and avalanches of neuronal activity. Saddle-node and supercritical Hopf bifurcations are the mechanisms of...

At an optimal value of the noise intensity, the maximum variability in rebound burst durations is observed and referred to as a response stochastic incoherence. A general mechanism underlying this phenomenon is given, being different from those reported so far in excitable systems. It is shown to be determined by (i) the monotonous reduction of the hysteresis responsible for bursting caused by ...