There is growing evidence in favor of the temporal-coding hypothesis that temporal correlation of neuronal discharges may serve to bind distributed neuronal activity into unique representations and, in particular, that theta (3.5-7.5 Hz) and delta (0.5 < 3.5 Hz) oscillations facilitate information coding. The theta- and delta-rhythms are shown to be involved in various sleep stages, and during anesthesia, they undergo changes with the depth of anesthesia. We introduce a thalamocortical model of interacting neuronal ensembles to describe phase relationships between theta- and delta-oscillations, especially during deep and light anesthesia. Asymmetric and long-range interactions among the thalamocortical neuronal oscillators are taken into account. The model results are compared with experimental observations. The delta- and theta-activities are found to be separately generated and are governed by the thalamus and cortex, respectively. Changes in the degree of intraensemble and interensemble synchrony imply that the neuronal ensembles inhibit information coding during deep anesthesia and facilitate it during light anesthesia.

We have identified the existence of globally clustered chimera states in delay-coupled oscillator populations and find that these states can breathe periodically and aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.

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Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N-coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically .

Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multi-clustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely periodic, aperiodic, long-and short-period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.