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Journal articles on the topic 'Stochastic cycle'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Netzer, Corinna, Michal Pasternak, Lars Seidel, Frédéric Ravet, and Fabian Mauss. "Computationally efficient prediction of cycle-to-cycle variations in spark-ignition engines." International Journal of Engine Research 21, no. 4 (2019): 649–63. http://dx.doi.org/10.1177/1468087419856493.

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Cycle-to-cycle variations are important to consider in the development of spark-ignition engines to further increase fuel conversion efficiency. Direct numerical simulation and large eddy simulation can predict the stochastics of flows and therefore cycle-to-cycle variations. However, the computational costs are too high for engineering purposes if detailed chemistry is applied. Detailed chemistry can predict the fuels’ tendency to auto-ignite for different octane ratings as well as locally changing thermodynamic and chemical conditions which is a prerequisite for the analysis of knocking comb

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2

Bashkirtseva, Irina, and Lev Ryashko. "Stochastic Bifurcations and Noise-Induced Chaos in a Dynamic Prey–Predator Plankton System." International Journal of Bifurcation and Chaos 24, no. 09 (2014): 1450109. http://dx.doi.org/10.1142/s0218127414501090.

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We consider the stochastic Truscott–Brindley dynamical model of the interacting populations of prey and predator. We study a new phenomenon of the stochastic cycle splitting. In a zone of Canard cycles, using the stochastic sensitivity function technique, we find a critical value of the parameter corresponding to the supersensitive cycle. In the neighborhood of this critical value, a comparative parametrical analysis of the phenomenon of the stochastic cycle splitting is performed. It is shown that the bifurcation of the stochastic cycle splitting is accompanied by the noise-induced chaotizati

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3

Brandenburg, Axel, and Gustavo Guerrero. "Cycles and cycle modulations." Proceedings of the International Astronomical Union 7, S286 (2011): 37–48. http://dx.doi.org/10.1017/s1743921312004619.

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AbstractSome selected concepts of the solar activity cycle are reviewed. Cycle modulations through a stochastic α effect are being identified with limited scale separation ratios. Three-dimensional turbulence simulations with helicity and shear are compared at two different scale separation ratios. In both cases the level of fluctuations shows relatively little variation with the dynamo cycle. Prospects for a shallow origin of sunspots are discussed in terms of the negative effective magnetic pressure instability. Tilt angles of bipolar active regions are discussed as a consequence of shear ra

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BASHKIRTSEVA, IRINA, LEV RYASHKO, and EUDOKIA SLEPUKHINA. "NOISE-INDUCED OSCILLATING BISTABILITY AND TRANSITION TO CHAOS IN FITZHUGH–NAGUMO MODEL." Fluctuation and Noise Letters 13, no. 01 (2014): 1450004. http://dx.doi.org/10.1142/s0219477514500047.

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Stochastic dynamics of the FitzHugh–Nagumo (FHN) neuron model in the limit cycles zone is studied. For weak noise, random trajectories are concentrated in the small neighborhood of the unforced deterministic cycle. As the noise intensity increases, in the Canard-like cycles zone of the FHN model, a bundle of the stochastic trajectories begins to split into two parts. This phenomenon is investigated using probability density functions for the distribution of random trajectories. It is shown that the intensity of noise generating this splitting bifurcation significantly depends on the stochastic

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BASHKIRTSEVA, I., L. RYASHKO, and P. STIKHIN. "NOISE-INDUCED BACKWARD BIFURCATIONS OF STOCHASTIC 3D-CYCLES." Fluctuation and Noise Letters 09, no. 01 (2010): 89–106. http://dx.doi.org/10.1142/s0219477510000095.

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We study stochastically forced multiple limit cycles of nonlinear dynamical systems in a period-doubling bifurcation zone. Noise-induced transitions between separate parts of the cycle are considered. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibili

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6

SOWERS, RICHARD B. "STOCHASTIC AVERAGING NEAR LONG HETEROCLINIC ORBITS." Stochastics and Dynamics 07, no. 02 (2007): 187–228. http://dx.doi.org/10.1142/s0219493707001974.

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We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically "glueing" together behavior of periodic orbits in the boundary layer near the heteroclinic cycle. Here, we adapt the analysis of [10] to allow for "long" heteroclinic cycles.

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7

YU. RYAGIN, MIKHAIL, and LEV B. RYASHKO. "THE ANALYSIS OF THE STOCHASTICALLY FORCED PERIODIC ATTRACTORS FOR CHUA'S CIRCUIT." International Journal of Bifurcation and Chaos 14, no. 11 (2004): 3981–87. http://dx.doi.org/10.1142/s0218127404011600.

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This report shows the results of sensitivity analysis for Chua's circuit periodic attractors under small disturbances. Sensitivity analysis is based on the quasipotential method. Quasipotential's first approximation in the neighborhood of the limit cycle is defined by the matrix of orbital quadratic form, named stochastic sensitivity function (SSF). SSF is defined for the points of the nonperturbed limit cycle and can be computed using the numerical algorithm. Stochastic sensitivity of the limit cycles for the Chua's circuit period doubling cascade is investigated. The growth of the stochastic

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8

Melchionna, Andrew. "Stochastic sandpile on a cycle." Journal of Physics A: Mathematical and Theoretical 55, no. 19 (2022): 195001. http://dx.doi.org/10.1088/1751-8121/ac61b9.

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Abstract In the stochastic sandpile (SS) model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability 0 < p < 1 of not moving. These interactions continue until each site has no more than one particle on it. We provide a formal coupling between the SS and the activated random walk models, and we use the coupling to show that for the SS with n particles on the cycle graph Z n , the system stabilizes in O(n 3) time for all initial particle configurations, provided that p(n) tends

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9

Luvsantseren, Purevdolgor, Enkhbayar Purevjav, and Khenmedeh Lochin. "Stochastic simulation of cell cycle." Advanced Studies in Biology 5 (2013): 1–9. http://dx.doi.org/10.12988/asb.2013.13001.

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10

Balasubramanian, K., V. Parameswaran, and S. B. Rao. "Characterization of Cycle Stochastic Graphs." Electronic Notes in Discrete Mathematics 15 (May 2003): 36. http://dx.doi.org/10.1016/s1571-0653(04)00520-7.

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11

Pichor, Katarzyna, and Ryszard Rudnicki. "One and two-phase cell cycle models." BIOMATH 8, no. 1 (2019): 1905261. http://dx.doi.org/10.11145/j.biomath.2019.05.261.

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In this review paper we present deterministic and stochastic one and two-phase models of the cell cycle. The deterministic models are given by partial differential equations of the first order with time delay and space variable retardation. The stochastic models are given by stochastic iterations or by piecewise deterministic Markov processes. We study asymptotic stability and sweeping of stochastic semigroups which describe the evolution of densities of these processes. We also present some results concerning chaotic behaviour of models and relations between different types of models.

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12

Vellela, Melissa, and Hong Qian. "On the Poincaré–Hill cycle map of rotational random walk: locating the stochastic limit cycle in a reversible Schnakenberg model." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2115 (2009): 771–88. http://dx.doi.org/10.1098/rspa.2009.0346.

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Recent studies on stochastic oscillations mostly focus on the power spectral analysis. However, the power spectrum yields information only on the frequency of oscillation and cannot differentiate between a stable limit cycle and a stable focus. The cycle flux, introduced by Hill (Hill 1989 Free energy transduction and biochemical cycle kinetics ), is a quantitative measure of the net movement over a closed path, but it is impractical to compute for all possible cycles in systems with a large state space. Through simple examples, we introduce concepts used to quantify stochastic oscillation, su

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13

Jia, Gaofeng, and Paolo Gardoni. "Stochastic life-cycle analysis: renewal-theory life-cycle analysis with state-dependent deterioration stochastic models." Structure and Infrastructure Engineering 15, no. 8 (2019): 1001–14. http://dx.doi.org/10.1080/15732479.2019.1590424.

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14

BASHKIRTSEVA, IRINA, LEV RYASHKO, and PAVEL STIKHIN. "NOISE-INDUCED CHAOS AND BACKWARD STOCHASTIC BIFURCATIONS IN THE LORENZ MODEL." International Journal of Bifurcation and Chaos 23, no. 05 (2013): 1350092. http://dx.doi.org/10.1142/s0218127413500922.

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We study the phenomena of stochastic D- and P-bifurcations of randomly forced limit cycles for the Lorenz model. As noise intensity increases, regular multiple limit cycles of this model in a period-doubling bifurcations zone are deformed to be stochastic attractors that look chaotic (D-bifurcation) and their multiplicity is reduced (P-bifurcation). In this paper for the comparative investigation of these bifurcations, the analysis of Lyapunov exponents and stochastic sensitivity function technique are used. A probabilistic mechanism of backward stochastic bifurcations for cycles of high multi

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15

Ambler, Steve, and Alain Paquet. "Stochastic Depreciation and the Business Cycle." International Economic Review 35, no. 1 (1994): 101. http://dx.doi.org/10.2307/2527092.

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16

Kalpazidou, S. "Cycle representations of denumerable stochastic matrices." Stochastic Analysis and Applications 16, no. 5 (1998): 895–906. http://dx.doi.org/10.1080/07362999808809568.

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17

Kalpazidou, S., and Joel E. Cohen. "Orthogonal cycle transforms of stochastic matrices." Circuits Systems and Signal Processing 16, no. 3 (1997): 363–74. http://dx.doi.org/10.1007/bf01246718.

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18

Bhadana, Jyoti, Md Zubbair Malik, and R. K. Brojen Singh. "Universality in stochastic enzymatic futile cycle." Applied Mathematical Modelling 74 (October 2019): 658–67. http://dx.doi.org/10.1016/j.apm.2019.05.008.

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19

Karolewska, Karolina, and Bogdan Ligaj. "Verification of the method of equivalent amplitude determination based on two - parameter fatigue characteristic." MATEC Web of Conferences 182 (2018): 02022. http://dx.doi.org/10.1051/matecconf/201818202022.

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In the most causes the loads which are affected on structural components are various over time and their character changes is stochastic. The stochastic character of operational loads of construction elements in various machine types is depended on many factors, included : work forces variability, environmental conditions, physical properties of components etc. Fatigue life calculation for this type of loads are conducted on the basis of determined sinusoidal cycles set through to use of the cycles counting method. The cycles which are contained to the sinusoidal cycles set are characterized b

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20

Wang, Zi-Fan, Jie Jiang, and Jing-Xiu Wang. "Observation-based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability." Astrophysical Journal 984, no. 2 (2025): 183. https://doi.org/10.3847/1538-4357/adc72d.

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Abstract Intercycle variations in the series of 11 yr solar activity cycles have a significant impact on both the space environment and climate. Whether solar cycle variability is dominated by deterministic chaos or stochastic perturbations remains an open question. Distinguishing between the two mechanisms is crucial for predicting solar cycles. Here we reduce the solar dynamo process responsible for the solar cycle to a one-dimensional iterative map, incorporating recent advances in the observed nonlinearity and stochasticity of the cycle. We demonstrate that deterministic chaos is absent in

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21

HUANG, DONGWEI, HONGLI WANG, and YINGFEI YI. "BIFURCATIONS IN A STOCHASTIC BUSINESS CYCLE MODEL." International Journal of Bifurcation and Chaos 20, no. 12 (2010): 4111–18. http://dx.doi.org/10.1142/s0218127410028227.

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We introduce a stochastic business cycle model and study the underlying stochastic Hopf bifurcations with respect to probability densities at different parameter values. Our analysis is based on the calculation of the largest Lyapunov exponent via multiplicative ergodic theorem and the theory of boundary analysis for quasi-nonintegrable Hamiltonian systems. Some numerical simulations of the model are performed.

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22

MELNIK, RODERICK V. N., XILIN WEI, and GABRIEL MORENO–HAGELSIEB. "NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS." Journal of Biological Systems 17, no. 03 (2009): 425–60. http://dx.doi.org/10.1142/s0218339009002879.

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Cell cycles are fundamental components of all living organisms and their systematic studies extend our knowledge about the interconnection between regulatory, metabolic, and signaling networks, and therefore open new opportunities for our ultimate efficient control of cellular processes for disease treatments, as well as for a wide variety of biomedical and biotechnological applications. In the study of cell cycles, nonlinear phenomena play a paramount role, in particular in those cases where the cellular dynamics is in the focus of attention. Quantification of this dynamics is a challenging t

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23

Engel, Maximilian, and Christian Kuehn. "A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations." Communications in Mathematical Physics 386, no. 3 (2021): 1603–41. http://dx.doi.org/10.1007/s00220-021-04077-z.

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AbstractFor an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be characterized as stable manifolds foliating neighborhoods of the limit cycle or as level sets of an isochron map. In recent years, there has been a lively discussion in the mathematical physics community on how to define isochrons for stochastic oscillations, i.e. limit cycles or heteroclinic cycles exposed to stochastic noise. The main discussion has concerned

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24

Biswas, Akash. "Exploring the predictability of the solar cycle from the polar field rise rate: Results from observations and simulations." Proceedings of the International Astronomical Union 19, S365 (2023): 148–53. https://doi.org/10.1017/s1743921323005045.

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AbstractThe inherent stochastic and nonlinear nature of the solar dynamo makes the strength of the solar cycles vary in a wide range, making it difficult to predict the strength of an upcoming solar cycle. Recently, our work has shown that by using the observed correlation of the polar field rise rate with the peak of polar field at cycle minimum and amplitude of following cycle, an early prediction can be made. In a follow-up study, we perform SFT simulations to explore the robustness of this correlation against variation of meridional flow speed, and against stochastic fluctuations of BMR ti

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25

Widianto, Eko, Firman Herdiansyah, Muhammad Burhannudinnur, Suryo Prakoso, and Benyamin Benyamin. "STOCHASTIC POROSITY MODELING IN VOLCANIC RESERVOIR JATIBARANG FORMATION." Journal of Geoscience Engineering & Energy 2, no. 2 (2021): 114. http://dx.doi.org/10.25105/jogee.v2i2.9993.

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Jatibarang Formation known as interesting volcanic reservoir in North West Java Basin. The reservoir was characterized by altered and naturally fractured that has significantly producing light oil. The volcanic Jatibarang reservoir consist of 3 volcanic cycles that are cycle 1, cycle 2 and cycle 3 with 16 faults configuration. Total and Fracture porosity modeling was conducted to determine secondary porosity distribution using stochastic method. Lithofacies and property lateral variation were generated to visualize geological model. Total porosity was estimated using formation evaluation. Natu

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26

Jiang, Jie. "Nonlinear and stochastic mechanisms of the solar cycle and their implications for the cycle prediction." Proceedings of the International Astronomical Union 19, S365 (2023): 98–106. https://doi.org/10.1017/s1743921324000097.

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AbstractSolar activity shows an 11-year (quasi)periodicity with a pronounced, but limited variability of the cycle amplitudes. The properties of active region (AR) emergence play an important role in the modulation of solar cycles and are our central concern in building a model for predicting future cycle(s) in the framework of the Babcock–Leighton (BL)-type dynamo. The emergence of ARs has the property that strong cycles tend to have higher mean latitudes and lower tilt angle coefficients. Their non-linear feedbacks on the solar cycle are referred to as latitudinal quenching and tilt quenchin

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27

Li, Longbiao. "A Micromechanical Fatigue Limit Stress Model of Fiber-Reinforced Ceramic-Matrix Composites under Stochastic Overloading Stress." Materials 13, no. 15 (2020): 3304. http://dx.doi.org/10.3390/ma13153304.

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Fatigue limit stress is a key design parameter for the structure fatigue design of composite materials. In this paper, a micromechanical fatigue limit stress model of fiber-reinforced ceramic-matrix composites (CMCs) subjected to stochastic overloading stress is developed. The fatigue limit stress of different carbon fiber-reinforced silicon carbide (C/SiC) composites (i.e., unidirectional (UD), cross-ply (CP), 2D, 2.5D, and 3D C/SiC) is predicted based on the micromechanical fatigue damage models and fatigue failure criterion. Under cyclic fatigue loading, the fatigue damage and fracture unde

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28

Posadas, Sergio, and Eugene P. Paulo. "Stochastic Simulation Of A Commander's Decision Cycle." Military Operations Research 8, no. 2 (2003): 21–43. http://dx.doi.org/10.5711/morj.8.2.21.

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29

Okabe, Yurie, and Masaki Sasai. "Stable Stochastic Dynamics in Yeast Cell Cycle." Biophysical Journal 93, no. 10 (2007): 3451–59. http://dx.doi.org/10.1529/biophysj.107.109991.

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30

Zhang, Yuping, Minping Qian, Qi Ouyang, Minghua Deng, Fangting Li, and Chao Tang. "Stochastic model of yeast cell-cycle network." Physica D: Nonlinear Phenomena 219, no. 1 (2006): 35–39. http://dx.doi.org/10.1016/j.physd.2006.05.009.

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31

Felber, S., H. P. Breuer, F. Petruccione, J. Honerkamp, and K. P. Hofmann. "Stochastic simulation of the transducin GTPase cycle." Biophysical Journal 71, no. 6 (1996): 3051–63. http://dx.doi.org/10.1016/s0006-3495(96)79499-7.

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32

Medvedev, Georgi S. "Synchronization of coupled stochastic limit cycle oscillators." Physics Letters A 374, no. 15-16 (2010): 1712–20. http://dx.doi.org/10.1016/j.physleta.2010.02.031.

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33

Olofsson, Peter, and Thomas O. McDonald. "A stochastic model of cell cycle desynchronization." Mathematical Biosciences 223, no. 2 (2010): 97–104. http://dx.doi.org/10.1016/j.mbs.2009.11.003.

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34

Woodhouse, Francis G., Aden Forrow, Joanna B. Fawcett, and Jörn Dunkel. "Stochastic cycle selection in active flow networks." Proceedings of the National Academy of Sciences 113, no. 29 (2016): 8200–8205. http://dx.doi.org/10.1073/pnas.1603351113.

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Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and

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35

Jenab, Kouroush, Kaveh Salehi Gilani, and Sareh Shafiei Monfared. "Stochastic cycle time analysis in robotic cells." International Journal of Industrial and Systems Engineering 5, no. 2 (2010): 129. http://dx.doi.org/10.1504/ijise.2010.030744.

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36

Itoh, Yoshiaki, and Kei-ichi Tainaka. "Stochastic limit cycle with power-law spectrum." Physics Letters A 189, no. 1-2 (1994): 37–42. http://dx.doi.org/10.1016/0375-9601(94)90815-x.

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37

Đorđević, Jasmina, Marija Milošević, and Nenad Šuvak. "Non-linear stochastic model for dopamine cycle." Chaos, Solitons & Fractals 177 (December 2023): 114220. http://dx.doi.org/10.1016/j.chaos.2023.114220.

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Sanders, Sara, Kunaal Joshi, Petra Anne Levin, and Srividya Iyer-Biswas. "Beyond the average: An updated framework for understanding the relationship between cell growth, DNA replication, and division in a bacterial system." PLOS Genetics 19, no. 1 (2023): e1010505. http://dx.doi.org/10.1371/journal.pgen.1010505.

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Our understanding of the bacterial cell cycle is framed largely by population-based experiments that focus on the behavior of idealized average cells. Most famously, the contributions of Cooper and Helmstetter help to contextualize the phenomenon of overlapping replication cycles observed in rapidly growing bacteria. Despite the undeniable value of these approaches, their necessary reliance on the behavior of idealized average cells masks the stochasticity inherent in single-cell growth and physiology and limits their mechanistic value. To bridge this gap, we propose an updated and agnostic fr

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Agrawal, Prachi, Talari Ganesh, and Ali Wagdy Mohamed. "Application of Water Cycle Algorithm to Stochastic Fractional Programming Problems." International Journal of Swarm Intelligence Research 13, no. 1 (2022): 1–21. http://dx.doi.org/10.4018/ijsir.2022010101.

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This paper presents an application of Water Cycle algorithm (WCA) in solving stochastic programming problems. In particular, Linear stochastic fractional programming problems are considered which are solved by WCA and solutions are compared with Particle Swarm Optimization, Differential Evolution, and Whale Optimization Algorithm and the results from literature. The constraints are handled by converting constrained optimization problem into an unconstrained optimization problem using Augmented Lagrangian Method. Further, a fractional stochastic transportation problem is examined as an applicat

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Soltani, Mohammad, and Abhyudai Singh. "Effects of cell-cycle-dependent expression on random fluctuations in protein levels." Royal Society Open Science 3, no. 12 (2016): 160578. http://dx.doi.org/10.1098/rsos.160578.

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Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We analyse a model where a stable protein is synthesized in random bursts, and the frequency with which bursts occur varies within the cell cycle. Formulae quantifying the extent of fluctuations in the protein copy number are derived and decomposed into components arising from the cell cycle and stochastic processes. The latter stochastic component represents

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Hu, Hui Bin, Li Jun Cao, Shu Xiao Chen, and Xin Wen Cao. "Stochastic Fatigue Reliability Analysis for Torsion Shaft of Military Tracked Vehicles." Applied Mechanics and Materials 543-547 (March 2014): 199–202. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.199.

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There are coupled cases of high-cycle fatigue and low-cycle fatigue in torsion shaft of military tracked vehicles. To accurately analyze the stochastic fatigue reliability of torsion shaft, a new kind of decoupling method for high-cycle fatigue and low-cycle fatigue was firstly put forward. Probability fatigue accumulation damage theory and nominal stress method were combined to analyze high-cycle fatigue. Random response surface method was adopted to fit the life distribution function for low-cycle fatigue. To obtain the high-cycle and low-cycle stochastic fatigue reliability, probability fat

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Kato, Yuzuru, Jinjie Zhu, Wataru Kurebayashi, and Hiroya Nakao. "Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory." Mathematics 9, no. 18 (2021): 2188. http://dx.doi.org/10.3390/math9182188.

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The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable sys

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Mircea, Gabriela, Mihaela Neamt¸u, and Dumitru Opris. "The Kaldor–Kalecki stochastic model of business cycle." Nonlinear Analysis: Modelling and Control 16, no. 2 (2011): 191–205. http://dx.doi.org/10.15388/na.16.2.14105.

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This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stochastic model, the dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given to illustrate our theoretical results.

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Xu, Chaoqun, Sanling Yuan, and Tonghua Zhang. "Stochastic Sensitivity Analysis for a Competitive Turbidostat Model with Inhibitory Nutrients." International Journal of Bifurcation and Chaos 26, no. 10 (2016): 1650173. http://dx.doi.org/10.1142/s021812741650173x.

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A stochastic model of turbidostat in which two microorganism species compete for an inhibitory growth-limiting nutrient is considered. In the deterministic case, the model has rich dynamics: a coexistence equilibrium and the washout equilibrium can be simultaneously stable, and a stable limit cycle may exist. In the stochastic case, a phenomenon of noise-induced extinction occurs. Namely, the stochastic trajectory near the deterministic coexistence equilibrium will tend to the washout equilibrium. Based on the stochastic sensitivity function technique, in this paper, we construct the confidenc

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YANG, MINGHAO, ZHIQIANG LIU, LI LI, et al. "IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS." International Journal of Bifurcation and Chaos 19, no. 02 (2009): 453–85. http://dx.doi.org/10.1142/s0218127409023135.

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Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show t

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46

Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.2307/3214149.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.1017/s0021900200040286.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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Carroll, Michael S., and Jan-Marino Ramirez. "Cycle-by-cycle assembly of respiratory network activity is dynamic and stochastic." Journal of Neurophysiology 109, no. 2 (2013): 296–305. http://dx.doi.org/10.1152/jn.00830.2011.

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Rhythmically active networks are typically composed of neurons that can be classified as silent, tonic spiking, or rhythmic bursting based on their intrinsic activity patterns. Within these networks, neurons are thought to discharge in distinct phase relationships with their overall network output, and it has been hypothesized that bursting pacemaker neurons may lead and potentially trigger cycle onsets. We used multielectrode recording from 72 experiments to test these ideas in rhythmically active slices containing the pre-Bötzinger complex, a region critical for breathing. Following synaptic

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Lin, Jie, and Debbie A. Niemeier. "An exploratory analysis comparing a stochastic driving cycle to California's regulatory cycle." Atmospheric Environment 36, no. 38 (2002): 5759–70. http://dx.doi.org/10.1016/s1352-2310(02)00695-7.

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Adams, Fred C., and Anthony M. Bloch. "Hill's equation with small fluctuations: Cycle to cycle variations and stochastic processes." Journal of Mathematical Physics 54, no. 3 (2013): 033511. http://dx.doi.org/10.1063/1.4795351.

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