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Understanding synchronous and traveling-wave oscillations, particularly as they relate to transitions between different types of behavior, is a central problem in modeling biological systems. Here, we address this problem in the context of central pattern generators (CPGs). We use contraction theory to establish the global stability of a traveling-wave or synchronous oscillation, determined by the type of coupling. This opens the door to better design of coupling architectures to create the desired type of stable oscillations. We then use coupling that is both amplitude and phase dependent to create either globally stable synchronous or traveling-wave solutions. Using the CPG motor neuron network of a leech as an example, we show that while both traveling and synchronous oscillations can be achieved by several types of coupling, the transition between different types of behavior is dictated by a specific coupling architecture. In particular, it is only the "repulsive" but not the commonly used phase or rotational coupling that can explain the transition to high-frequency synchronous oscillations that have been observed in the heartbeat pattern generator of a leech. This shows that the overall dynamics of a CPG can be highly sensitive to the type of coupling used, even for coupling architectures that are widely believed to produce the same qualitative behavior. [ABSTRACT FROM AUTHOR]

Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process. [ABSTRACT FROM AUTHOR]

We investigate disease extinction in an epidemic model described by a birth-death process. We show that, in the absence of vaccination, the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed random vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters.

Complete chaotic synchronization of end lasers has been observed in a line of mutually coupled, time-delayed system of three lasers, with no direct communication between the end lasers. The present paper uses ideas from generalized synchronization to explain the complete synchronization in the presence of long coupling delays, applied to a model of mutually coupled semiconductor lasers in a line. These ideas significantly simplify the analysis by casting the stability in terms of the local dynamics of each laser. The variational equations near the synchronization manifold are analyzed, and used to derive the synchronization condition that is a function of parameters. The results explain and predict the dependence of synchronization on various parameters, such as time delays, strength of coupling and dissipation. The ideas can be applied to understand complete synchronization in other chaotic systems with coupling delays and no direct communication between synchronized subsystems.

Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultraharmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures generate an in-phase high-frequency state by coupling with an array in an antiphase state. The underlying mechanism for the creation and stability of the ultraharmonic oscillations is analyzed. A class of interarray coupling is shown to create a stable, in-phase oscillation having frequency that increases linearly with the number of oscillators, but with an amplitude that stays fairly constant. The analysis of the theory is illustrated by numerical simulation of coupled arrays of Stuart-Landau limit cycle oscillators.