2,528 research outputs found
Pattern Formation Induced by Time-Dependent Advection
We study pattern-forming instabilities in reaction-advection-diffusion
systems. We develop an approach based on Lyapunov-Bloch exponents to figure out
the impact of a spatially periodic mixing flow on the stability of a spatially
homogeneous state. We deal with the flows periodic in space that may have
arbitrary time dependence. We propose a discrete in time model, where reaction,
advection, and diffusion act as successive operators, and show that a mixing
advection can lead to a pattern-forming instability in a two-component system
where only one of the species is advected. Physically, this can be explained as
crossing a threshold of Turing instability due to effective increase of one of
the diffusion constants
Dynamics of multi-frequency oscillator ensembles with resonant coupling
We study dynamics of populations of resonantly coupled oscillators having
different frequencies. Starting from the coupled van der Pol equations we
derive the Kuramoto-type phase model for the situation, where the natural
frequencies of two interacting subpopulations are in relation 2:1. Depending on
the parameter of coupling, ensembles can demonstrate fully synchronous
clusters, partial synchrony (only one subpopulation synchronizes), or
asynchrony in both subpopulations. Theoretical description of the dynamics
based on the Watanabe-Strogatz approach is developed.Comment: 12 page
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