Networks of neurons, which form central pattern generators (CPGs), are important for controlling animal behaviors. Of special interest are configurations or CPG motifs composed of reciprocally inhibited neurons, such as half-center oscillators (HCOs). Bursting rhythms of HCOs are shown to include stable synchrony or in-phase bursting. This in-phase bursting can co-exist with anti-phase bursting, commonly expected as the single stable state in HCOs that are connected with fast non-delayed synapses. The finding contrasts with the classical view that reciprocal inhibition has to be slow or time-delayed to synchronize such bursting neurons. Phase-locked rhythms are analyzed via Lyapunov exponents estimated with variational equations, and through the convergence rates estimated with Poincar\'e return maps. A new mechanism underlying multistability is proposed that is based on the spike interactions, which confer a dual property on the fast non-delayed reciprocal inhibition; this reveals the role of spikes in generating multiple co-existing phase-locked rhythms. In particular, it demonstrates that the number and temporal characteristics of spikes determine the number and stability of the multiple phase-locked states in weakly coupled HCOs. The generality of the multistability phenomenon is demonstrated by analyzing diverse models of bursting networks with various inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, the Purkinje neuron model and Fitzhugh-Rinzel phenomenological model. Finally, hypothetical and experiment-based CPGs composed of HCOs are investigated. This study is relevant for various applications that use CPGs such as robotics, prosthetics, and artificial intelligence.

Electrical and optical characterizations of heterostructures and thin films based on group III-V compound semiconductors are presented. Optical properties of GaMnN thin films grown by Metalorganic Chemical Vapor Deposition (MOCVD) on GaN/Sapphire templates were investigated using IR reflection spectroscopy. Experimental reflection spectra were fitted using a non - linear fitting algorithm, and the high frequency dielectric constant (ε∞), optical phonon frequencies of E1(TO) and E1(LO), and their oscillator strengths (S) and broadening constants (Γ) were obtained for GaMnN thin films with different Mn fraction. The high frequency dielectric constant (ε∞) of InN thin films grown by the high pressure chemical vapor deposition (HPCVD) method was also investigated by IR reflection spectroscopy and the average was found to vary between 7.0 - 8.6. The mobility of free carriers in InN thin films was calculated using the damping constant of the plasma oscillator. The terahertz detection capability of n-type GaAs/AlGaAs Heterojunction Interfacial Workfunction Internal Photoemission (HEIWIP) structures was demonstrated. A threshold frequency of 3.2 THz (93 µm) with a peak responsivity of 6.5 A/W at 7.1 THz was obtained using a 0.7 µm thick 1E18 cm−3 n - type doped GaAs emitter layer and a 1 µm thick undoped Al(0.04)Ga(0.96)As barrier layer. Using n - type doped GaAs emitter layers, the possibility of obtaining small workfunctions (∆) required for terahertz detectors has been successfully demonstrated. In addition, the possibility of using GaN (GaMnN) and InN materials for terahertz detection was investigated and a possible GaN base terahertz detector design is presented. The non - linear behavior of the Inter Pulse Time Intervals (IPTI) of neuron - like electric pulses triggered externally in a GaAs/InGaAs Multi Quantum Well (MQW) structure at low temperature (~10 K) was investigated. It was found that a grouping behavior of IPTIs exists at slow triggering pulse rates. Furthermore, the calculated correlation dimension reveals that the dimensionality of the system is higher than the average dimension found in most of the natural systems. Finally, an investigation of terahertz radiation efect on biological system is reported.