We consider two identical oscillators with time delayed coupling, modelled by a system of delay differential equations. We reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. By analyzing the phase model, we show how the time delay affects the stability of phase-locked periodic solutions and causes stability switching of in-phase and ...

We present various bursting wave forms that are obtained from a simple model of the Hodgkin-Huxley type. The model is a typical example whose characteristics can be discussed through the concept of potential with active areas. A potential function is able to provide a global landscape for dynamics of a model, and the dynamics are explained in relation to the disposition of the active areas on t...

The ability to move in complex environments is one of the most important features of humans and animals. In this work, we exploit a bio-inspired method to generate different gaits in a bipedal locomotion system. We use the 4-cell CPG model developed by Pinto [21]. This model has been established on symmetric coupling between the cells which are responsible for generating oscillatory signals. Th...

We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent dif...

Phase response curve (PRC) of an oscillatory neuron describes the response of the neuron to external perturbation. The PRC is useful to predict synchronized dynamics of neurons; hence, its measurement from experimental data attracts increasing interest in neural science. This paper introduces a Bayesian method for estimating PRCs from data, which allows for the correlation of errors in explanat...

We continue the analysis of the network of symmetrically coupled cells modeling central pattern generators (CPG) for quadruped locomotion proposed by Golubitsky, Stewart, Buono and Collins by studying secondary gaits. Secondary gaits are modeled by output signals from the CPG where each cell emits one of two different output signals along with exact phase shifts. Examples of secondary gaits are...

We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. Similarly to the case of harmonic inputs, these neurons exhibit a resonant behavior also for pulsed inputs. We interpret this phenomenon in terms of the subthreshold response of the neuron. In the presence of dynamical trains of input pulses whose frequency vari...

The dynamical behavior of the neurons directly depends on transition from resting to spiking states. These transitions show different types bifurcations and has periods. are also affected by temperature exposure ionic channels. To understand such effects, we investigate Morris-Lecar (ML) neuron model with calcium, potassium leak current presented ML is considered electromagnetic field coupling ...

In this note, we want to show (a) how the statistics of synaptic input influences the read-out of stored intrinsic properties for two-dimensional model neurons and (b) the effects of network topology on synchronization, i.e. the correlations of synaptic input generated in the network. This theoretical work relates to the biological properties of neuromodulation by presynaptic and postsynaptic e...

The modeling of real neuronal networks by close-to-biology circuits can contribute to a better understanding these from circuit theoretical point view. This potentially lead novel design principles for electrical circuits. process involves the mimicking measured activity, which is often only available as calcium imaging recordings. In this work, we develop wave digital model emulator capable ca...