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Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…
A dynamical effect of coherent backscattering is predicted theoretically and supported by computer simulations: The distribution of single-mode delay times of waves reflected by a disordered waveguide depends on whether the incident and…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can…
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…
The paper presents an improved mass balancing procedure for fast rotating machinery, while it is being rotated at speeds considerably slower than the "critical speeds", where dangerously high vibration amplitudes may arise. By utilizing…
Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve non linear interactions between waves. In this…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
A change in the sign of the frequency of a wave between two inertial reference frames corresponds to a reversal of the phase velocity. Yet from the point of view of the relation $E=\hbar\omega$, a positive quantum of energy apparently…
We present a general theory for noise-induced corrections to the angular velocity of spiral waves. Stochasticity produces two second-order effects: an instantaneous term from heterogeneity that always slows rotation, and an orbital-drift…
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation…
Rhythmogenesis, which is critical for many biological functions, involves a transition to coherent activity through cell-cell communication. In the absence of centralized coordination by specialized cells (pacemakers), competing oscillating…
We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a…
We introduce a mechanism that can both hold and amplify electromagnetic waves by rapidly changing the permittivity of the medium during the wave travel from a positive to a dispersionless (i.e. non-Foster) negative value and then back…
Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions…
Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems.…
Over a sufficiently long period of time, or from an appropriate distance, the motion of many swimmers can appear smooth, with their trajectories appearing almost ballistic in nature and slowly varying in character. These long-time…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…