807 research outputs found
Sequential escapes: onset of slow domino regime via a saddle connection
We explore sequential escape behaviour of coupled bistable systems under the
influence of stochastic perturbations. We consider transient escapes from a
marginally stable "quiescent" equilibrium to a more stable "active"
equilibrium. The presence of coupling introduces dependence between the escape
processes: for diffusive coupling there is a strongly coupled limit (fast
domino regime) where the escapes are strongly synchronised while for
intermediate coupling (slow domino regime) without partially escaped stable
states, there is still a delayed effect. These regimes can be associated with
bifurcations of equilibria in the low-noise limit. In this paper we consider a
localized form of non-diffusive (i.e pulse-like) coupling and find similar
changes in the distribution of escape times with coupling strength. However we
find transition to a slow domino regime that is not associated with any
bifurcations of equilibria. We show that this transition can be understood as a
codimension-one saddle connection bifurcation for the low-noise limit. At
transition, the most likely escape path from one attractor hits the escape
saddle from the basin of another partially escaped attractor. After this
bifurcation we find increasing coefficient of variation of the subsequent
escape times
Complex and unexpected dynamics in simple genetic regulatory networks
Peer reviewedPublisher PD
Fast and slow domino regimes in transient network dynamics
It is well known that the addition of noise to a multistable dynamical system
can induce random transitions from one stable state to another. For low noise,
the times between transitions have an exponential tail and Kramers' formula
gives an expression for the mean escape time in the asymptotic limit. If a
number of multistable systems are coupled into a network structure, a
transition at one site may change the transition properties at other sites. We
study the case of escape from a "quiescent" attractor to an "active" attractor
in which transitions back can be ignored. There are qualitatively different
regimes of transition, depending on coupling strength. For small coupling
strengths the transition rates are simply modified but the transitions remain
stochastic. For large coupling strengths transitions happen approximately in
synchrony - we call this a "fast domino" regime. There is also an intermediate
coupling regime some transitions happen inexorably but with a delay that may be
arbitrarily long - we call this a "slow domino" regime. We characterise these
regimes in the low noise limit in terms of bifurcations of the potential
landscape of a coupled system. We demonstrate the effect of the coupling on the
distribution of timings and (in general) the sequences of escapes of the
system.Comment: 3 figure
Diversity-induced resonance in a system of globally coupled linear oscillators
The purpose of this paper to analyze in some detail the arguably simplest
case of diversity-induced reseonance: that of a system of globally-coupled
linear oscillators subjected to a periodic forcing. Diversity appears as the
parameters characterizing each oscillator, namely its mass, internal frequency
and damping coefficient are drawn from a probability distribution. The main
ingredients for the diversity-induced-resonance phenomenon are present in this
system as the oscillators display a variability in the individual responses but
are induced, by the coupling, to synchronize their responses. A steady state
solution for this model is obtained. We also determine the conditions under
which it is possible to find a resonance effect.Comment: Reported at the XI International Workshop "Instabilities and
Nonequilibrium Structures" Vina del Mar (Chile
Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.
Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate
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