16 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
Modelling and Synchronisation of Delayed Packet-Coupled Oscillators in Industrial Wireless Sensor Networks
In this paper, a Packet-Coupled Oscillators (PkCOs) synchronisation protocol
is proposed for time-sensitive Wireless Sensor Networks (WSNs) based on
Pulse-Coupled Oscillators (PCO) in mathematical biology. The effects of delays
on synchronisation performance are studied through mathematical modelling and
analysis of packet exchange and processing delays. The delay compensation
strategy (i.e., feedforward control) is utilised to cancel delays effectively.
A simple scheduling function is provided with PkCOs to allocate the packet
transmission event to a specified time slot, by configuring reference input of
the system to a non-zero value, in order to minimise the possibility of packet
collision in synchronised wireless networks. The rigorous theoretical proofs
are provided to validate the convergence and stability of the proposed
synchronisation scheme. Finally, the simulations and experiments examine the
effectiveness of PkCOs with delay compensation and scheduling strategies. The
experimental results also show that the proposed PkCOs algorithm can achieve
synchronisation with the precision of ( tick)