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2009 Index IEEE Transactions on Automatic Control Vol. 54

2009 IEEE Transactions on Automatic Control  
Mukaidani, H., +, TAC Sept. 2009 2244-2250 Partial differential equations A Sampled-Data Singularly Perturbed Boundary Control for a Heat Conduction System With Noncollocated Observation. Cheng, M.  ...  Aswani, A., +, TAC Aug. 2009 1913- 1918 Singular Perturbations and Lindblad-Kossakowski Differential Equations.  ...  Hopper. 1779 -1793 Time-Optimal Path Tracking for Robots: A Convex Optimization Approach.  ... 
doi:10.1109/tac.2009.2037798 fatcat:4ilhkzss6jc63ersjzi47hiwgu

Singular renormalization group approach to SIS problems

Ning Sun, ,School of Mathematics, Jilin University, Changchun 130012, China, Shaoyun Shi, Wenlei Li, ,School of Mathematics & State Key Laboratory of Automotive, Simulation and Control, Jilin University, Changchun 130012, China
2017 Discrete and continuous dynamical systems. Series B  
By introducing a singular parameter, the system can be viewed as a singularly perturbed problem.  ...  large comparing to the diffusion rates of infected and susceptible populations; (ii) the diffusion rate of the susceptible population approaches zero.  ...  renormalized expansion (10) with respect to ζ, we derive the following renormalization group equations up to O(ε) dV (ζ) dζ = −εR 1 (V (ζ)) + εe τ A R 2 (V (ζ)). (11) Suppose now that we can solve RG  ... 
doi:10.3934/dcdsb.2020073 fatcat:eadpyht5jvherlxfutgbat2wqu

Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

Timothy Halpin-Healy, Yi-Cheng Zhang
1995 Physics reports  
Let us now have a glimpse at that list: stochastic differential equations, dynamic and functional renormalization groups, Langevin and Fokker-Planck equations, fluctuation-dissipation theorem, Bethe ansatz  ...  Note, too, the recent renormalization group study [ Mi94] concerning overlap distributions for the many-dimensional DPRM.  ...  Acknowledgments This review started with a suggestion by Itamar Procaccia a couple of years ago.  ... 
doi:10.1016/0370-1573(94)00087-j fatcat:kwz2xwvx2zaxdbawslxuq5jij4

Dirichlet Form Theory and its Applications

Sergio Albeverio, Zhen-Qing Chen, Masatoshi Fukushima, Michael Röckner
2014 Oberwolfach Reports  
to specific areas of probability.  ...  Theory of Dirichlet forms is one of the main achievements in modern probability theory. It provides a powerful connection between probabilistic and analytic potential theory.  ...  Acknowledgement: The MFO and the workshop organizers would like to thank the National Science Foundation for supporting the participation of junior researchers in the workshop by the grant DMS-1049268,  ... 
doi:10.4171/owr/2014/48 fatcat:cp5yvda4qzdifefbxuhv4knyva

Homoclinic and Heteroclinic Bifurcations in Vector Fields [chapter]

Ale Jan Homburg, Björn Sandstede
2010 Handbook of Dynamical Systems  
Finally, a few related topics, such as topological moduli, numerical algorithms, variational methods, and extensions to singularly perturbed and infinitedimensional systems, are reviewed briefly. where  ...  Furthermore, v j (µ) is a multiple of the eigenvector of f u (p(µ), µ) associated with ν j (µ) for j = s, u. In addition, there is a constant > 0 so that and analogously for h u (t; µ).  ...  A typical delay differential equation is of the forṁ u(t) = f (u(t), u(t − τ )), u ∈ R n , where τ > 0 is the temporal delay.  ... 
doi:10.1016/s1874-575x(10)00316-4 fatcat:fadh4mnuw5erlpcikmoiqoa6oe

Spatiotemporal dynamics of continuum neural fields

Paul C Bressloff
2011 Journal of Physics A: Mathematical and Theoretical  
We survey recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields.  ...  Neural fields model the large-scale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations whose associated integral kernels represent the spatial  ...  PCB is also grateful to Professor Steve Coombes (University of Nottingham) for his careful reading of the manuscript.  ... 
doi:10.1088/1751-8113/45/3/033001 fatcat:sj7ezyxblnhm7p4mklvghnyqlu

Transition to blow-up in a reaction–diffusion model with localized spike solutions

2017 European journal of applied mathematics  
For certain singularly perturbed two-component reaction–diffusion systems, the bifurcation diagram of steady-state spike solutions is characterized by a saddle-node behaviour in terms of some parameter  ...  More specifically, we use a blend of asymptotic analysis, linear stability theory, and full numerical computations to analyse a wide variety of dynamical instabilities, and ultimately finite-time blow-up  ...  In the analysis, we use a dynamical rescaling approach, based on a near-similarity group transformation, to construct a solution to (1.3) that has finite-time blow-up at x = x 0 .  ... 
doi:10.1017/s0956792517000043 fatcat:xkfb524mfzgavieay3aurp7kca

Page 891 of Mathematical Reviews Vol. 27, Issue Index [page]

Mathematical Reviews  
H.; et al., 95m:34118 Wysocki, Hubert A matrix operational calculus. (English summary) 954:44015 Xiang, Xiao Ling Existence of periodic solutions for a class of delay partial differential equations.  ...  English and Chinese summaries) 95¢:47086 Yang, Zuo Dong (with Fan, Xi Zhi) Existence of positive solutions to boundary value problems for a class of quasilinear second-order equations. (Chinese.  ... 

Page 606 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
Kolmogorov-Armnold-Moser renormalization-group approach to the breakup of invariant tori in Hamiltonian systems. (English summary) 99e:58150 Cheban, D. N.  ...  (English summary) 99¢:34170 — On the existence of almost periodic solutions of a singularly perturbed differential equation with piecewise constant argument.  ... 

Spatiotemporal order out of noise

Francesc Sagués, José M. Sancho, Jordi García-Ojalvo
2007 Reviews of Modern Physics  
The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential  ...  The consideration of those fluctuations supposes to deal with noisy quantities whose variance might at times be a sizable fraction of their mean levels.  ...  ACKNOWLEDGMENTS We thank all our colleagues who have collaborated with us in the study of noise-induced phenomena throughout the years.  ... 
doi:10.1103/revmodphys.79.829 fatcat:d73gtihm4rah5ogvkmmlhxnzke

Non-Hermitian Physics [article]

Yuto Ashida, Zongping Gong, Masahito Ueda
2020 arXiv   pre-print
We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach.  ...  , as well as a number of instructive examples.  ...  Acknowledgments We are grateful to Yohei Fuji, Takeshi  ... 
arXiv:2006.01837v1 fatcat:ol3sszpdvneejg7mgywm7abj64

General nucleation theory with inhibition for chemically reacting systems

Jonathan A. D. Wattis, Peter V. Coveney
1997 Journal of Chemical Physics  
A systematic procedure is developed for extracting from the full model, which comprises an infinite set of differential equations, a low dimensional dynamical system containing only a few key equations  ...  From these macroscopic equations it is possible to deduce the most important elements of the reaction scheme, and to isolate the rate-determining stages.  ...  ACKNOWLEDGMENTS The authors would like to thank John Garside, Roger Davey and John Billingham for helpful comments and advice.  ... 
doi:10.1063/1.474018 fatcat:bd5szq26yjhc5j2q7rbj2ybopm

Page 715 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Smoothness of the strongly stable invariant foliation. 2001¢:37025 Cherevko, I. M. On the asymptotics of integral manifolds of singularly perturbed systems with delay. (Ukrainian.  ...  Averaging of some boundary value problems for systems of differential equations with variable delay. (Ukrainian.  ... 

Cosmic Acceleration from Causal Backreaction in a Smoothly Inhomogeneous Universe [article]

Brett Bochner
2012 arXiv   pre-print
The observed acceleration results from the combined effect of innumerable local perturbations, due to individually virialized systems, overlapping together in a smoothly-inhomogeneous adjustment of the  ...  the angular scale of the Cosmic Microwave Background to within a reasonable proximity of their Concordance values.  ...  ' which they assumed to be unphysical and thus removed via a "bare mass" renormalization step.  ... 
arXiv:1109.4686v3 fatcat:7hprmjrvhvdtje34tg34n7aeei

Page 773 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Stepwise asymptotics of solutions of a class of singularly perturbed nonlinear problems with free surfaces. (Ukrainian. English, Russian and Ukrainian summaries) Barrett, John W.'  ...  A symbolic computation method to decide the completeness of the solutions to the system of linear partial differential equations. (Chinese.  ... 
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