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Stability and bifurcation properties of the algorithms for keeping of differential equations solutions on the required level [article]

Yu.V. Troshchiev
2016 arXiv   pre-print
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished.  ...  An equation, which can be the base equation for investigation of the idealized algorithms properties, is constructed.  ...  An equation is constructed under assumption that the systems keep or almost keep some definite properties, and this equation can be the main equation for investigation of the idealized algorithms properties  ... 
arXiv:1601.00112v1 fatcat:3nvb766otzhshevasexxigbr3i

Three-dimensional equilibria in axially symmetric tokamaks

P. R. Garabedian
2006 Proceedings of the National Academy of Sciences of the United States of America  
T ϭ BB Ϫ ͑B 2 ͞2 ϩ p͒I enables one to put the MHD equations describing force balance in the conservation form  ...  For both tokamaks and stellarators, correct solutions of the relevant differential equations have discontinuities associated with islands and current sheets.  ...  The algorithm implemented in the TRAN code solves the quasineutrality equation by requiring that Fourier coefficients of the densities n i and n e of ions and electrons coincide.  ... 
doi:10.1073/pnas.0609569103 pmid:17159158 pmcid:PMC1748209 fatcat:uwcq6yoetjcotbywtcdr2aw3pq

Effect of two forms of feedback on the performance of the Rate Control Protocol (RCP) [article]

Abuthahir Abuthahir, Nizar Malangadan, Gaurav Raina
2019 arXiv   pre-print
Further, using Poincaré normal forms and center manifold theory, we investigate two nonlinear properties, namely, the type of Hopf bifurcation and the asymptotic stability of the bifurcating limit cycles  ...  The analytical results reveal that the removal of queue feedback could enhance both stability and convergence properties.  ...  Thus, future research should also include an in-depth analysis of the impact of queue feedback on the performance of the system with multiple time delays, and for a variety of flow arrival and departure  ... 
arXiv:1906.00374v1 fatcat:pl26idogoffctpazjqcrmtq6ya

Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

P.S. Mandal, M. Banerjee
2012 Mathematical Modelling of Natural Phenomena  
Finally we construct a stochastic differential equation model corresponding to the deterministic model to understand the role of demographic stochasticity.  ...  Exhaustive numerical simulation of the stochastic model reveals the large amplitude fluctuation in the population of fish and Pelicans for certain parameter values.  ...  The research work of first author is supported by the C. S. I. R., India. We are thankful to the anonymous reviewer for his/her constructive comments to improve the our work significantly.  ... 
doi:10.1051/mmnp/20127308 fatcat:k72mrdzo5beulg2532syiiksuy

Inverse bifurcation analysis: application to simple gene systems

James Lu, Heinz W Engl, Peter Schuster
2006 Algorithms for Molecular Biology  
This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability  ...  desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems.  ...  for comments on the paper.  ... 
doi:10.1186/1748-7188-1-11 pmid:16859561 pmcid:PMC1570349 fatcat:7hrfwgcjnzakjdockojhzw3m6a

Coarse Brownian dynamics for nematic liquid crystals: Bifurcation, projective integration, and control via stochastic simulation

C. I. Siettos, M. D. Graham, I. G. Kevrekidis
2003 Journal of Chemical Physics  
Through this approach, both stable and unstable branches of the equilibrium bifurcation diagram are obtained for the Doi model of LCPs and their coarse stability is estimated.  ...  We demonstrate how time-integration of stochastic differential equations (i.e.  ...  The stability results here are consistent with those dictated by bifurcation theory: solutions on the subcritical prolate branch are unstable between U*ϽUϽU cr and regain stability past the turning point  ... 
doi:10.1063/1.1572456 fatcat:4u6keo2ksvdnjnnjyt4qztiswy

An Integral 1-D Eulerian–Lagrangian Method and Its Application to a Hydrodynamic River Network

Shuai Yuan, Jianzhong Zhou, Dechao Hu, Sipeng Zhu
2020 Water  
It is difficult for a one-dimensional river network hydrodynamic model to manage bifurcations.  ...  physical equations at bifurcations.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/w12020542 fatcat:gpro35me55gdvp6mfnnwvlsrou

Voltage Stability Toolbox for Power System Education and Research

Saffet Ayasun, Chika O. Nwankpa, Harry G. Kwatny
2006 IEEE Transactions on Education  
VST is a very flexible tool for load flow, small-signal and transient stability, and bifurcation analysis.  ...  After a brief summary of power system model and local bifurcations, the paper illustrates the capabilities of VST using the IEEE 14-bus system as an example and describes its successful integration into  ...  For the DAE model of power systems, the load-flow equations for PV and PQ buses have to be solved in advance of solving the differential equations of the generators.  ... 
doi:10.1109/te.2006.879798 fatcat:vr2hmsnldzfexipugr3ux3xztu

Modeling of Self-Organizing Systems: An Overview

Richard Holzer, Patrick Wüchner, Hermann De Meer
2010 Electronic Communications of the EASST  
On the micro level, the behavior of each entity and the interaction between different object must be described by the model.  ...  This paper gives a systematic overview on modeling formalisms suitable for modeling self-organizing systems. We distinguish between micro-level modeling and macro-level modeling.  ...  Therefore, the behavior s v of the node v is just the local orbit of the internal state of v which results from the solution of the differential equation (B4) and the hops given by (B5).  ... 
doi:10.14279/tuj.eceasst.27.385 dblp:journals/eceasst/HolzerWM10 fatcat:zg7zhbzgmrdw7j2gacdo6fu5ma

Equation-free analysis of agent-based models and systematic parameter determination

Spencer A. Thomas, David J.B. Lloyd, Anne C. Skeldon
2016 Physica A: Statistical Mechanics and its Applications  
This algorithm automatically detects outliers based on the dynamics of the underlying system enabling both an order of magnitude reduction in ensemble size and continuation of systems at much higher levels  ...  Yet few tools are currently available for the systematic analysis of ABM behaviour. Numerical continuation and bifurcation analysis is a wellestablished tool for the study of deterministic systems.  ...  Acknowledgements The authors thank Giovanni Samaey for useful comments on an earlier draft of this manuscript.  ... 
doi:10.1016/j.physa.2016.07.043 fatcat:bn2novyhufbbxbffqhviibvyiu

Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice-gas model with lateral interactions

Alexei G. Makeev, Dimitrios Maroudas, Athanassios Z. Panagiotopoulos, Ioannis G. Kevrekidis
2002 Journal of Chemical Physics  
Through numerical continuation and stability analysis, we construct one-and two-parameter coarse bifurcation diagrams.  ...  We present a computer-assisted study of "coarse" stability/bifurcation calculations for kinetic Monte Carlo simulators using the so-called coarse timestepper approach presented in A. G. Makeev, D.  ...  Within the context of numerical bifurcation theory, one can construct augmented systems whose solutions are precisely bifurcation points, i.e., points of neutral stability for the original systems.  ... 
doi:10.1063/1.1512274 fatcat:q7ozmolgrvchbfkepuaw7rhkgm

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

Giuseppe Piccardo, Francesco D'Annibale, Daniele Zulli
2014 Continuum Mechanics and Thermodynamics  
The most original contributions of Angelo Luongo in the context of perturbation methods, linear and nonlinear dynamics and control, elastic buckling and structural analysis, bifurcation and stability of  ...  In fact, even when the work seems purely algorithmic, speculation on the physical and mechanical aspects of the problem is always present, providing new interpretations and innovative openings to a careful  ...  Thus, he exploited a formal analogy between the perturbative equations for (linear) eigenvalue sensitivity and the (nonlinear) bifurcation equations to implement new algorithms for these latter.  ... 
doi:10.1007/s00161-014-0388-z fatcat:y4pm5optrbdw7cpwld4l4wzc2q

Non-Linear Real And Complex Modes Of Conewise Linear Systems

L. Zuo, A. Curnier
1994 Journal of Sound and Vibration  
Then the non-linear real and complex modes are obtained for both non-gyroscopic and gyroscopic cases, by means of analytical or numerical tools.  ...  Conewise (piecewise) linear, non-gyroscopic and gyroscopic autonomous systems are studied in detail First, the general properties of such systems are examined.  ...  Schatzman for showing us how to shorten the proof of the second proposition concerning the positive homogeneity of the solutions.  ... 
doi:10.1006/jsvi.1994.1277 fatcat:bqnvssqiq5eyteyyncze674eui

A numerical Liapunov-Schmidt method with applications to Hopf bifurcation on a square

Peter Ashwin, Klaus B{öhmer, Zhen Mei
1995 Mathematics of Computation  
We discuss an iterative method for calculating the reduced bifurcation equation of the Liapunov-Schmidt method and its numerical approximation.  ...  This method is used to calculate reduced equations at Hopf bifurcation of the two-dimensional Brusselator equations on a square with Neumann and Dirichlet boundary conditions.  ...  Acknowledgments We thank Jacques Furter for helpful conversations. P.A. was supported by the Royal Society European Exchange Program (UK) and M.Z. was supported by the DFG (Germany).  ... 
doi:10.1090/s0025-5718-1995-1284661-x fatcat:scbnvscbf5bpbhuordjru3kk7i

Design of the DEMO Fusion Reactor Following ITER

Paul R Garabedian, Geoffrey B McFadden
2009 Journal of Research of the National Institute of Standards and Technology  
Test particle runs of the TRAN transport code suggest that for quasineutrality to prevail in tokamaks a certain minimum level of 3D asymmetry of the magnetic spectrum is required which is comparable to  ...  Runs of the NSTAB nonlinear stability code show there are many three-dimensional (3D) solutions of the advanced tokamak problem subject to axially symmetric boundary conditions.  ...  This numerical solution of the MHD equations has converged to the level of round off error in double precision, assuring existence, uniqueness, and stability.  ... 
pmid:27504224 pmcid:PMC4651607 fatcat:i5sdaexgyfcm7eisv7vuxwv22y
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