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Multi-Delay Differential Equations: A Taylor Expansion Approach [article]

Philip Doldo, Jamol Pender
2020 arXiv   pre-print
It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay  ...  In this paper, we present some single-delay approximations to a multi-delay system obtained via a Taylor expansion as well as formulas for their critical delays which are used to approximate where the  ...  Despite the complexity to obtain analytic results for multi-delay differential equations, some analytic results do exist for certain classes of DDE systems that have two or three delays.  ... 
arXiv:2012.05005v1 fatcat:56kq25xp4bfaxijbp26uk4q2yy

Approximate solution of a model of biological immune responses incorporating delay

A. C. Fowler
1981 Journal of Mathematical Biology  
at earlier times, is considered from an analytic standpoint.  ...  A method of approximation based on a consideration of the asymptotic limit of"large" delay in the antibody response is shown to be applicable, and to give results similar to those obtained numerically  ...  Approximate solutions for ordinary differential equations often rely on the presence of a small parameter, which may be used to obtain an asymptotic representation of the solution.  ... 
doi:10.1007/bf00276864 pmid:7334284 fatcat:o67a55owqbejneh5dqdisu3k7m

Brownian Molecules Formed by Delayed Harmonic Interactions

Daniel Geiss, Klaus Kroy, Viktor Holubec
2019 New Journal of Physics  
Furthermore, we thank Thomas Ihle and Sarah Loos for discussion.  ...  Acknowledgments We acknowledge funding by Deutsche Forschungsgemeinschaft (DFG) via SPP 1726/1 and support from the German Research Foundation (DFG) and Universität Leipzig within the program of Open Access  ...  For a nonzero delay, based on the approximate solution (17) to the Langevin equation (15) assuming r , Î -¥ ¥ ( )and x(t) = 0 for t < 0, we have found that the one-time PDF P P x t P x t x , , ,0 1 1  ... 
doi:10.1088/1367-2630/ab3d76 fatcat:zavgi2dafzbphehnphh7cigaaq

Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Zhang, The stability of neutral stochastic delay differential equations with Poisson jumps by fixed points 3115-3120 Liu, Y.-C., J. Zhang and G.-H.  ...  Wen, Dissipativity of one-leg methods for neutral delay integro-differential equations 165-173 Liu, Q., Modified Gram-Schmidt-based methods for block downdating the Cholesky factorization 1897-1905 Liu  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

author index volumes 141-150

2003 Journal of Computational and Applied Mathematics  
For the sake of simplicity and uniformity, all names beginning with articles or prepositions are listed as if written as single words.) PII: S 0 3 7 7 -0 4 2 7 ( 0 2 ) 0 0 8 4 3 -9  ...  of differential-equation solutions: universal approximation method 146 (2002) 443-457 Lenferink, W., A second order scheme for a time-dependent, singularly perturbed convection-diffusion equation  ...  Hozumi, Mathematical proof of closed form expressions for finite difference approximations based on Taylor series 150 (2003) 303-309 Khan, M.A.H., High-order differential approximants 149 (2002) 457-468  ... 
doi:10.1016/s0377-0427(02)00843-9 fatcat:erfaawky35awbnyddoudgikksu

Brownian Molecules Formed by Delayed Harmonic Interactions [article]

Daniel Geiss, Klaus Kroy, Viktor Holubec
2019 arXiv   pre-print
For completeness, we include a comprehensive discussion of the analytical solution procedure for systems of linear stochastic delay differential equations in finite dimension, and new results for covariance  ...  For N ≤ 3 , we characterize its collective behavior analytically, by solving the pertinent stochastic delay-differential equations, and for N>3 by Brownian dynamics simulations.  ...  The result is C(τ ) = ω −1 σ η(s)x (s) = 0.5ω −1 σσ , where the last equality comes after inserting the formal solution (B.11) for x(t) into the average, using the covariance of the noise, and noticing  ... 
arXiv:1905.07192v2 fatcat:f6p5nz5r3vamphhz7qpvxfrc6y

Path integrals in fluctuating markets

Frederic D. R. Bonnet, Andrew G. Allison, Derek Abbott, Zoltan Gingl
2004 Noise in Complex Systems and Stochastic Dynamics II  
In this short note we propose an approach for calculating option prices in financial markets in the framework of path integrals.  ...  We explore how the path integral methods may be used to study financial markets quantitatively and we also suggest a method in calculating transition probabilities for option pricing using real data in  ...  The interpretation of a stochastic differential equation arises when dealing with a multiplicative stochastic differential equation, also called a multiplicative Langevin equation dY dt = f (Y ) + g(Y  ... 
doi:10.1117/12.548795 fatcat:vjyh6ojmibemfd6uqsvjpkfika

2019 Index IEEE Transactions on Automatic Control Vol. 64

2019 IEEE Transactions on Automatic Control  
., +, TAC Feb. 2019 654- 669 Delay-differential systems Analytic Solution of a Delay Differential Equation Arising in Cost Func- tionals for Systems With Distributed Delays.  ...  ., +, TAC Nov. 2019 4705-4710 On the Asymptotic Behavior for Neutral Stochastic Differential Delay Equations.  ... 
doi:10.1109/tac.2020.2967132 fatcat:o2hd2t4jz5fbpkcemjt5aj7xrm

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks

Fernando Antoneli, Renata C. Ferreira, Marcelo R.S. Briones
2016 Mathematical Biosciences  
Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory  ...  Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation  ...  Hence, we have a discrete-time version of the rate equations with an explicit dependence on the stochastic processes γn, δn and ξn without any a priori specified type of probability distributions other  ... 
doi:10.1016/j.mbs.2016.03.008 pmid:27036626 fatcat:g6mvurjrzrhyllf5mpxopap2im

Master Index Volumes 1-100

2002 Stochastic Processes and their Applications  
Appl. 86 (2000) uchler, U., On stationary solutions of delay differential equations driven by a L!  ...  of solutions for one-dimensional stochastic differential equations 21 (1985) 45 Gualtierotti, A.F., A class of stochastic processes with a law generalizing a nondecomposable law on the real line 13 (1982  ...  -L., On a stochastic wave equation in two space dimensions: regularity of the solution and its density 86 (2000) 141 Millet, A., see Chenal, F. 72 (1997 ) 161 Millet, A., see Mazziotto, G. 21 (1985 58  ... 
doi:10.1016/s0304-4149(02)00154-0 fatcat:5zmghyapt5d5fp272vy3x63bbq

The equivalence between weak and strong purifying selection [article]

Benjamin H Good, Michael M Desai
2012 arXiv   pre-print
Here, we demonstrate a natural symmetry between weak and strong selection, in which the effects of many weakly selected mutations on patterns of molecular evolution are equivalent to a smaller number of  ...  By introducing a coarse-grained "effective selection coefficient," we derive an explicit mapping between weakly selected populations and their strongly selected counterparts, which allows us to make accurate  ...  B.H.G. acknolwedges support from a National Science Foundation Graduate Research Fellowship.  ... 
arXiv:1210.4500v1 fatcat:npgqwhqt6zfbfem5rt2oibzuae

On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm [chapter]

Timothy P. Hubbard, Harry J. Paarsch
2014 Handbook of Computational Economics  
We provide a formal comparison of the performance of these numerical methods (based on speed and accuracy) and suggest ways in which they can be improved and extended as well as applied to new settings  ...  We describe and compare numerical methods used to approximate equilibrium bid functions in models of auctions as games of incomplete information.  ...  Paarsch gratefully acknowledges that some of the research for this paper was completed while he was a visiting research scholar at the Collegio Carlo Alberto in Moncalieri, Italy.  ... 
doi:10.1016/b978-0-444-52980-0.00002-5 fatcat:lg7vpreoa5bbjp4iodvsut62qy

Statistical mechanics of ecological systems: Neutral theory and beyond

Sandro Azaele, Samir Suweis, Jacopo Grilli, Igor Volkov, Jayanth R. Banavar, Amos Maritan
2016 Reviews of Modern Physics  
While there are a few reviews of NT oriented towards ecologists, our goal here is to review the quantitative results of NT and its extensions for physicists who are interested in learning what NT is, what  ...  We conclude the review by discussing how one might introduce realistic non-neutral elements into the current models.  ...  Based on pioneering work by McKane, Alonso and Solé (McKane et al., 2000) , an analytical solution was proposed for the ME when the size of both the local community and the meta-community was fixed (  ... 
doi:10.1103/revmodphys.88.035003 fatcat:pqnkywdgnng2lpin2ea4slvwya

Optimal Control of Spatial-Dynamic Processes: The Case of Biological Invasions

Rebecca S. Epanchin-Niell, James Wilen
2011 Social Science Research Network  
We develop a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal spatial-dynamic control strategies.  ...  We find that the optimal strategies depend in interesting ways on the shape of the landscape and the location, shape, and contiguity of the invasion.  ...  The state equation is often an ordinary differential equation that describes how the size or extent of the invasion varies over time as a function of itself and the quantity of control.  ... 
doi:10.2139/ssrn.1776244 fatcat:u7yq6bgqizfmxawvy5e6worute

New directions in stabilisation policies

Ralf Fendel
2004 PSL Quarterly Review  
In order to highlight the progress connected with the new class of models, it puts them into the context of former debates on stabilization policy, such as the Phillips curve dispute.  ...  Recently, a new class of macroeconomic business cycle models has emerged.  ...  In particular, parameter estimates imply an average price duration of one year for a firm, which is consistent with survey data (Taylor 1999a).  ... 
doaj:085c78b1494b46e29864ab507837581d fatcat:ao6ix5w35nc2noanejnyd3sq2q
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