In this letter, we study the memristor-based oscillators, and propose for the first time the method of calculating its PPV (Perturbation Projection Vector). In order to get PPV, we have deduced the formula to convert PRC (Phase Response Curve) to PPV. The conversion method is verified rigorously by comparing PPV obtained from PSS+PXF simulation and PRC calculated from transient simulation of tw...

Intracellular recordings have been made from ventilatory neurones in semi-isolated and isolated thoracic ganglia of the crab Carcinus during spontaneous switching between the two motor programmes underlying forward and reversed beating of the scaphognathites (SGs). Ventilatory reversals are dependent upon the central activation of two subgroups of motoneurones which are normally silent, and dif...

A neural network is considered which is designed as a system of phase oscillators and contains a central oscillator that interacts with a number of peripheral oscillators. Analytical and simulation methods are used to study the dynamics of the system that is conditioned by the interaction parameters and natural frequencies of the oscillators. The boundaries of parameter regions are found that c...

We show how a topological model which describes the stretching and squeezing mechanisms responsible for creating chaotic behavior can be extracted from the neural spike train data. The mechanism we have identified is the same one ("gateau roule," or jelly-roll) which has previously been identified in the Duffing oscillator [Gilmore and McCallum, Phys. Rev. E 51, 935 (1995)] and in a YAG laser [...

We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of fi...

A direct adaptive output feedback control design procedure is developed for highly uncertain nonlinear systems, that do not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension. In particular, we consider single-input/single-output nonlinear systems, whose output has known, but otherwise arbitrary relative degree. This includes systems with both...

Neural oscillations play an important role in normal brain activity, but also manifest during Parkinson's disease, epilepsy, and other pathological conditions. The contribution of these aberrant oscillations to the function of the surviving brain remains unclear. In recording from retina in a mouse model of retinal degeneration (RD), we found that the incidence of oscillatory activity varied ac...

In this paper we use a two-layer neural network for robust image segmentation. The rst layer is a locally coupled recurrent network. Using probabilistic measures, contextual information is incorporated eeectively through underlying coupling structures, which reduces and even resolves local ambiguities in images. The second layer is a LEGION (Locally Excitatory Globally Inhibitory Oscillator Net...

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, ...

Memristor-based oscillator is becoming promising thanks to its inherent NDR (Negative Differential Region) property and compact circuit structure. This paves the way to the large scale oscillatory neural network (ONN) and the realization of pattern recognition based on its global synchronization. However, the simulation of large scale ONN encounters the problem of long simulation time because o...