LOCBIF swMATH ID: 7928 Software Authors: Khibnik, Alexander I.; Kuznetsov, Yuri A.; Levitin, Victor V.; Nikolaev, Eugene V. Description: Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps. We present a numerical technique for the analysis of local bifurcations which is based on the continuation of structurally unstable invariant sets in a suitable phase-parameter space. The invariant sets involved in our study are equilibrium points and limit cycles of autonomous ODEs, periodic solutions of time-periodic nonautonomous ODEs, fixed points and periodic orbits of iterated maps. The more general concept of a continuation strategy is also discussed. It allows the analysis of various singularities of generic systems and of their mutual relationships. The approach is extended to codimension three singularities. We introduce several bifurcation functions and show how to use them to construct well-posed continuation problems. The described continuation technique is supported by an interactive graphical program called LOCBIF. We discuss briefly the concepts of the LOCBIF interface and give some examples of typical applications. Homepage: http://www.sgtnd.narod.ru/science/nummeth/bifsoft/content/eng/locbif.htm Keywords: numerical technique; analysis of local bifurcations; continuation of structurally unstable invariant sets; singularities; interactive graphical program; LOCBIF Related Software: AUTO; DSTool; AUTO-86; HomCont; PITCON; MATCONT; CONTENT; DDE-BIFTOOL; XPPAUT; AUTO2000; CL_MATCONT; Matlab; Mathematica; PLTMG; Torcont; XPPy; GitHub; SciPy; PSPManalysis; psSchur Cited in: 65 Publications all top 5 Cited by 106 Authors 8 Kooi, Bob W. 7 Kuznetsov, Yuri Alexandrovich 6 Govaerts, Willy J. F. 6 Kooijman, Sebastiaan A. L. M. 6 Moiola, Jorge Luis 5 Boer, Martin P. 4 Borisyuk, Roman M. 4 Feichtinger, Gustav 4 Khibnik, Alexander I. 4 Piccardi, Carlo 4 Roose, Dirk 3 Gatto, Marino 2 Auger, Pierre M. 2 Bolzoni, Luca 2 Bravo de la Parra, Rafael 2 Casagrandi, Renato 2 Chen, Guanrong 2 de Roos, André M. 2 Diekmann, Odo 2 Gragnani, Alessandra 2 Gyllenberg, Mats 2 Hommes, Cars H. 2 Itovich, Griselda R. 2 Jansen, Vincent A. A. 2 Kuijper, Lothar D. J. 2 Nikolaev, Eugene V. 2 Prskawetz, Alexia 2 Rinaldi, Sergio 2 Tuinstra, Jan 2 Wang, Hua O. 1 Abed, Eyad H. 1 Andreasen, Viggo 1 Ataullakhanov, Fazoil I. 1 Bees, Martin A. 1 Behrens, Doris A. 1 Berns, Daniel W. 1 Bonfili, P. A. 1 Borisyuk, Galina N. 1 Burylko, Oleksandr 1 Calandrini, Guillermo L. 1 Champneys, Alan R. 1 Chatterjee, Anindya 1 Chua, Leon Ong 1 Cochelin, Bruno 1 Cymbalyuk, Gennady S. 1 Dangelmayr, Gerhard 1 De Leo, Giulio A. 1 de Vries, Gerda 1 Dercole, Fabio 1 Dhooge, Annick 1 Dobson, Andrew P. 1 Doedel, Eusebius J. 1 Edwards, Andrew M. 1 Eirola, Timo 1 El Abdllaoui, Abderrahim 1 Ericsson, Stefan 1 Fiedler, Bernold 1 Forst, Christian V. 1 Gaunersdorfer, Andrea 1 Genesio, Roberto 1 Ghezzi, Luca Luigi 1 Goeree, Jacob K. 1 Gol’dshtein, Vladimir Mikhailovich 1 Greiner, Alfred 1 Guckenheimer, John M. 1 Guillot, Louis 1 Hartl, Richard F. 1 Haunschmied, Josef L. 1 Hofmann, Ulrich G. 1 Janovský, Vladimír 1 Kirchgässner, Klaus 1 Kooi, W. B. 1 Kort, Peter M. 1 Krapivnik, N. 1 Levin, Simon Asher 1 Levitin, Victor V. 1 Lobanov, Alekseĭ Ivanovich 1 Lust, Kurt 1 Luzyanina, Tatyana 1 McCauley, Edward 1 Mchich, Rachid 1 Meijer, Hil G. E. 1 Merrison-Hort, Robert 1 Metz, Johan A. Jacob 1 Mielke, Alexander 1 Milik, Alexandra 1 Morozova, O. L. 1 Nakaoka, Shinji 1 Njap, Felix 1 Pei, Lijun 1 Plecháč, Petr 1 Poggiale, Jean-Christophe 1 Sherman, Arthur S. 1 Sijnave, B. 1 Söderbacka, Gunnar 1 Spence, Alastair 1 Tesi, Alberto 1 Torresi, Ana M. L. 1 Troost, Tineke A. 1 Vergez, Christophe ...and 6 more Authors all top 5 Cited in 28 Serials 7 Mathematical Biosciences 6 Theoretical Population Biology 5 Journal of Mathematical Biology 4 Chaos, Solitons and Fractals 3 Automatica 3 SIAM Journal on Numerical Analysis 3 Journal of Economic Dynamics & Control 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Nonlinear Dynamics 2 Bulletin of Mathematical Biology 2 ACM Transactions on Mathematical Software 2 Applied Mathematics and Computation 2 European Journal of Operational Research 2 SIAM Journal on Scientific Computing 2 Journal of Biological Systems 1 Biological Cybernetics 1 Journal of the Franklin Institute 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Kybernetika 1 OR Spektrum 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Economics 1 Chaos 1 Mathematical Modelling of Natural Phenomena 1 The Journal of Mathematical Neuroscience 1 Journal of Theoretical Biology all top 5 Cited in 15 Fields 33 Dynamical systems and ergodic theory (37-XX) 32 Ordinary differential equations (34-XX) 31 Biology and other natural sciences (92-XX) 15 Numerical analysis (65-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Systems theory; control (93-XX) 3 Partial differential equations (35-XX) 2 Mechanics of particles and systems (70-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year