MFPT calculation for random walks in inhomogeneous networks

Wijesundera, Isuri; Halgamuge, Malka N.; Nirmalathas, Ampalavanapillai; Nanayakkara, Thrishantha

doi:10.1016/j.physa.2016.06.015

Cited by 7 publications

(6 citation statements)

References 45 publications

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“…When the system has several state space attractors, the application of the proposed method is not straight forward. We have addressed this limitation using the concept of identifying ‘network primitives’ with a case study of cyclone prediction in [29].…”

Section: Discussionmentioning

confidence: 99%

“…In the existence of bias, these two transport variables need to be modified in order to account for the potential fields or obstacles shaping these walks [26, 29]. As a measure of the density of the nodes (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…Starting with a collection of uniformly distributed node sets ( N = 50 × 50) on 2D space (a section of which is shown in Fig 4(a)), the nodes were moved around by adding a Normally distributed noise with a fixed standard deviation ( σ ) for each case as where ( x i , y i ) are the coordinates of the i th node without added noise (Fig 4(b)–4(d)). A network generated in this way becomes a ‘network primitive’ when the variance of transport properties at every node are negligible [29]. It is worth noting the importance of having the noise level fixed and low such that all nodes would still belong to the same primitive network.…”

Section: Methodsmentioning

confidence: 99%

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Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability

et al. 2018

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Idealized passive dynamic walkers (PDW) exhibit limit cycle stability at steady state. Yet in reality, uncertainty in ground interaction forces result in variability in limit cycles even for a simple walker known as the Rimless Wheel (RW) on seemingly even slopes. This class of walkers is called metastable walkers in that they usually walk in a stable limit cycle, though guaranteed to eventually fail. Thus, control action is only needed if a failure state (i.e. RW stopping down the ramp) is imminent. Therefore, efficiency of estimating the time to reach a failure state is key to develop a minimal intervention controller to inject just enough energy to overcome a failure state when required. Current methods use what is known as a Mean First Passage Time (MFPT) from current state (rotary speed of RW at the most recent leg collision) to an arbitrary state deemed to be a failure in the future. The frequently used Markov chain based MFPT prediction requires an absorbing state, which in this case is a collision where the RW comes to a stop without an escape. Here, we propose a novel method to estimate an MFPT from current state to an arbitrary state which is not necessarily an absorbing state. This provides freedom to a controller to adaptively take action when deemed necessary. We demonstrate the proposed MFPT predictions in a minimal intervention controller for a RW. Our results show that the proposed method is useful in controllers for walkers showing up to 44.1% increase of time-to-fail compared to a PID based closed-loop controller.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability

et al. 2018

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“…( 41) and (( 45)) tells us that the mean field is equal to the average of any single particle's position in some certain threshold. This allows us to study dynamic behaviors of systems among single particles through the the mean field, related to synchronous, mean first passing time (MFPT)(see the definition and related discussion by [29] and [30]), occurring of stochastic resonance, and significant difference on the output gain G for fractional dynamic systems by comparing with traditional dynamic systems with order of the derivative α being or closing the integer 1 in sections 3 and 4 below.…”

Section: Modelling Synchronization Among Mean Fields and General Part...mentioning

confidence: 99%

The mechanics of dynamic behaviors for SMEs’ growth by using fractional-order dynamic system approach

Ren

Yuan

2022

J. Finan. Eng.

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The goal of this paper is to establish a general framework for the development of small- or medium-sized enterprises’ (SMEs) growth path by using star-coupled stochastic dynamic system approach. The dynamic behaviors are related to the stochastic resonance (SR) phenomenon subject to multiplicative fluctuation and periodic force which could be interpreted as uncertain environments faced by SMEs (enterprises) during their growth process. The multiplicative noise is modeled as dichotomous noise (uncertainty under the innovation and capital paradigm) and the memory of risk environments is characterized by using fractional kernel function. By using the mathematical derivation, the analytical expressions for the first moment of the steady state response, the stability in the long-time limit in terms of (enterprises) systems’ asymptotic stability is obtained. Theoretic and simulation results show the nonmonotonic dependence between the output gain and the input signal frequency, noise parameters for SMEs dynamic behaviors. Furthermore, the fluctuation noise, the number of related parties (partners) for SMEs, and the fractional-order work together, producing more complex dynamic phenomena compared with the traditional integral-order systems (for enterprises). Finally, theoretical analyses with corresponding numerical simulations results established in this paper would provide a possible fundamental mathematical framework for the study of Schumpeter’s theory on the development for SMEs’ growth under the “innovation and capital paradigm” and related disciplines. In particular, the framework allows us, for the first time, to logically conclude that “in general, the ratio for SMEs’ growth successfully is around less than one-third”, this is actually consistent with what the market has been observing commonly in general.

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“…The other is to focus on learning how some intriguing dynamical behaviors are influenced by the underlying topological structure of complex networks [20,21]. Discussed behaviors occurring on complex networks have: (1) synchronization phenomena [22], (2) chaotic control for system identification [23], (3) percolation [24], (4) epidemic spreading [25] and (5) random walks [26] and so on.…”

Section: Introductionmentioning

confidence: 99%

Random walks on Fibonacci treelike models: emergence of power law

Ma,

Wang,

Yao

2019

Preprint

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In this paper, we propose a class of growth models, named Fibonacci trees F (t), with respect to the intrinsic advantage of Fibonacci sequence {F t }. First, we turn out model F (t) to have power-law degree distribution with exponent γ greater than 3. And then, we study analytically two significant indices correlated to random walks on networks, namely, both the optimal mean first-passage time (OM F P T ) and the mean first-passage time (M F P T ).We obtain a closed-form expression of OM F P T using algorithm 1. Meanwhile, algorithm 2 and algorithm 3 are introduced, respectively, to capture a valid solution to M F P T . We demonstrate that our algorithms are able to be widely applied to many network models with self-similar structure to derive desired solution to OM F P T or M F P T . Especially, we capture a nontrivial result that the M F P T reported by algorithm 3 is no longer correlated linearly with the order of model F (t).

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MFPT calculation for random walks in inhomogeneous networks

Cited by 7 publications

References 45 publications

Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability

Predicting the mean first passage time (MFPT) to reach any state for a passive dynamic walker with steady state variability

The mechanics of dynamic behaviors for SMEs’ growth by using fractional-order dynamic system approach

Random walks on Fibonacci treelike models: emergence of power law

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