Noise Induced Switching in Delayed Systems

Schwartz, Ira B.; Carr, Thomas W.; Billings, Lora; Dykman, M. I.

doi:10.21236/ada561020

Cited by 3 publications

(3 citation statements)

References 38 publications

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“…Such changes depend on the specifics of the individual models, and cannot be understood using the reduction described above. Precise results for large deviations in delayed Langevin equations have been obtained [30, 38]. However, the correct Langevin approximations of the models we consider here need to include delay in the diffusion term [39, 40]).…”

Section: Discussionmentioning

confidence: 99%

Transcriptional Delay Stabilizes Bistable Gene Networks

et al. 2013

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Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner.

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Section: Discussionmentioning

confidence: 99%

Transcriptional Delay Stabilizes Bistable Gene Networks

et al. 2013

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“…An extension of the approach leading to Eq. (35) to overdamped systems was compared with numerical simulations for a model system and good agreement was found in the whole range where the delay time was smaller than the relaxation time [66].…”

Section: Short Noise Correlation Timementioning

confidence: 90%

Large rare fluctuations in systems with delayed dissipation

Dykman

Schwartz

2012

Phys. Rev. E

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We study the probability distribution and the escape rate in systems with delayed dissipation that comes from the coupling to a thermal bath. To logarithmic accuracy in the fluctuation intensity, the problem is reduced to a variational problem. It describes the most probable fluctuational paths, which are given by acausal equations due to the delay. In thermal equilibrium, the most probable path passing through a remote state has time-reversal symmetry, even though one cannot uniquely define a path that starts from a state with given system coordinate and momentum. The corrections to the distribution and the escape activation energy for small delay and small noise correlation time are obtained in explicit form.

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“…Schwartz et. al [44] have demonstrated that the methodology introduced in section 2 can be adapted to write this system as a Hamiltonian system,…”

Section: Time Delayed Sdesmentioning

confidence: 99%

An iterative action minimizing method for computing optimal paths in stochastic dynamical systems

Lindley

Schwartz

2013

Physica D: Nonlinear Phenomena

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We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system. The numerical method presented here involves using an iterative scheme for solving a two-point boundary value problem for the Hamiltonian system. We validate our method by applying it to both continuous stochastic systems, such as nonlinear oscillators governed by the Duffing equation, and finite discrete systems, such as epidemic problems, which are governed by a set of master equations. Furthermore, we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations.

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Noise Induced Switching in Delayed Systems

Cited by 3 publications

References 38 publications

Transcriptional Delay Stabilizes Bistable Gene Networks

Transcriptional Delay Stabilizes Bistable Gene Networks

Large rare fluctuations in systems with delayed dissipation

An iterative action minimizing method for computing optimal paths in stochastic dynamical systems

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