Enhancing noise-induced switching times in systems with distributed delays

Kyrychko, Yuliya N.; Schwartz, Ira B.

doi:10.1063/1.5034106

Cited by 11 publications

(10 citation statements)

References 55 publications

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“…In a modified Stuart-Landau model [65] two distinct time delays induce instabilities that exhibit spatio-temporal pattern formation and turbulence [66]. In time delay systems with stateswitching the dynamics becomes more robust to noise, when two distinct time delays are incorporated [67].…”

Section: Multiple Constant Time Delaysmentioning

confidence: 99%

Chaos in time delay systems, an educational review

2019

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The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with it various kinds of chaotic phases. Which are then the possible types of time delays, induced chaotic states, and methods suitable to characterize the resulting dynamics? This review presents an overview of the field that includes an in-depth discussion of the most important results, of the standard numerical approaches and of several novel tests for identifying chaos. Special emphasis is placed on a structured representation that is straightforward to follow. Several educational examples are included in addition as entry points to the rapidly developing field of time delay systems.

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Section: Multiple Constant Time Delaysmentioning

confidence: 99%

Chaos in time delay systems, an educational review

2019

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“…Combining (16), (19), (24), and (38), we arrive at the final form of the linear noise approximation (LNA)…”

Section: The Inactive Protein Fluctuationmentioning

confidence: 99%

Postponing production exponentially enhances the molecular memory of a stochastic switch

Bokes

2020

Preprint

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Delayed production can substantially alter the qualitative behaviour of feedback systems. Motivated by stochastic mechanisms in gene expression, we consider a protein molecule which is produced in randomly timed bursts, requires an exponentially distributed time to activate, and then partakes in positive regulation of its burst frequency. Asymptotically analysing the underlying master equation in the large-delay regime, we provide tractable approximations to time-dependent probability distributions of molecular copy numbers. Importantly, the presented analysis demonstrates that positive feedback systems with large production delays can constitute a stable toggle switch even if they operate with low copy numbers of active molecules.

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“…For example, we have studied swarms with complex network topology, and quantified instabilities arising from heterogeneous topology in the number of local interactions each agents has [36]. We have examined the effects of communication delay and how environmental noise destabilizes self-organized patterns [37,38]. In addition, we have analyzed other environmental effects, such as range-dependent communication and surface geometry, as a function swarm control parameters [39,40].…”

Section: Introductionmentioning

confidence: 99%

Interacting Swarm Sensing and Stabilization

Schwartz,

Edwards,

Hindes

2021

Preprint

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Swarming behavior, where coherent motion emerges from the interactions of many mobile agents, is ubiquitous in physics and biology. Moreover, there are many efforts to replicate swarming dynamics in mobile robotic systems which take inspiration from natural swarms. In particular, understanding how swarms come apart, change their behavior, and interact with other swarms is a research direction of special interest to the robotics and defense communities. Here we develop a theoretical approach that can be used to predict the parameters under which colliding swarms form a stable milling state. Our analytical methods rely on the assumption that, upon collision, two swarms oscillate near a limit-cycle, where each swarm rotates around the other while maintaining an approximately constant density. Using our methods, we are able to predict the critical swarm-swarm interaction coupling (below which two colliding swarms merely scatter) for nearly aligned collisions as a function of physical swarm parameters. We show that the critical coupling corresponds to a saddle-node bifurcation of a limit-cycle in the constant-density approximation. Finally, we show preliminary results from experiments in which two swarms of micro UAVs collide and form a milling state, which is in general agreement with our theory.

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Enhancing noise-induced switching times in systems with distributed delays

Cited by 11 publications

References 55 publications

Chaos in time delay systems, an educational review

Chaos in time delay systems, an educational review

Postponing production exponentially enhances the molecular memory of a stochastic switch

Interacting Swarm Sensing and Stabilization

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