Guillot, Louis; Cochelin, Bruno; Vergez, Christophe A Taylor series-based continuation method for solutions of dynamical systems. (English) Zbl 1430.37099 Nonlinear Dyn. 98, No. 4, 2827-2845 (2019). MSC: 37M20 34E05 PDFBibTeX XMLCite \textit{L. Guillot} et al., Nonlinear Dyn. 98, No. 4, 2827--2845 (2019; Zbl 1430.37099) Full Text: DOI HAL
Pei, Lijun; Wang, Shuo Double Hopf bifurcation of differential equation with linearly state-dependent delays via MMS. (English) Zbl 1428.34127 Appl. Math. Comput. 341, 256-276 (2019). MSC: 34K60 34K18 34K20 37G05 34K23 PDFBibTeX XMLCite \textit{L. Pei} and \textit{S. Wang}, Appl. Math. Comput. 341, 256--276 (2019; Zbl 1428.34127) Full Text: DOI
Diekmann, Odo; Gyllenberg, Mats; Metz, J. A. J.; Nakaoka, Shinji; de Roos, Andre M. Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example. (English) Zbl 1208.92082 J. Math. Biol. 61, No. 2, 277-318 (2010); erratum ibid. 75, No. 1, 259-261 (2017). MSC: 92D40 34K20 37N25 92D25 45D05 65L05 PDFBibTeX XMLCite \textit{O. Diekmann} et al., J. Math. Biol. 61, No. 2, 277--318 (2010; Zbl 1208.92082) Full Text: DOI
Bolzoni, Luca; De Leo, Giulio A.; Gatto, Marino; Dobson, Andrew P. Body-size scaling in an SEI model of wildlife diseases. (English) Zbl 1209.92052 Theor. Popul. Biol. 73, No. 3, 374-382 (2008). MSC: 92D30 34C60 37N25 PDFBibTeX XMLCite \textit{L. Bolzoni} et al., Theor. Popul. Biol. 73, No. 3, 374--382 (2008; Zbl 1209.92052) Full Text: DOI
Dercole, Fabio BPcont: An auto driver for the continuation of branch points of algebraic and boundary-value problems. (English) Zbl 1173.65073 SIAM J. Sci. Comput. 30, No. 5, 2405-2426 (2008). MSC: 65P30 65Y15 65L10 37M20 37G15 65H20 65H10 PDFBibTeX XMLCite \textit{F. Dercole}, SIAM J. Sci. Comput. 30, No. 5, 2405--2426 (2008; Zbl 1173.65073) Full Text: DOI
Govaerts, W.; Ghaziani, R. Khoshsiar; Kuznetsov, Yu. A.; Meijer, H. G. E. Numerical methods for two-parameter local bifurcation analysis of maps. (English) Zbl 1155.65397 SIAM J. Sci. Comput. 29, No. 6, 2644-2667 (2007). MSC: 65P30 37G05 37M20 PDFBibTeX XMLCite \textit{W. Govaerts} et al., SIAM J. Sci. Comput. 29, No. 6, 2644--2667 (2007; Zbl 1155.65397) Full Text: DOI Link
Kooi, B. W.; Troost, T. A. Advantage of storage in a fluctuating environment. (English) Zbl 1118.92061 Theor. Popul. Biol. 70, No. 4, 527-541 (2006). MSC: 92D40 92D15 37N25 91A40 PDFBibTeX XMLCite \textit{B. W. Kooi} and \textit{T. A. Troost}, Theor. Popul. Biol. 70, No. 4, 527--541 (2006; Zbl 1118.92061) Full Text: DOI
Casagrandi, Renato; Bolzoni, Luca; Levin, Simon A.; Andreasen, Viggo The SIRC model and influenza A. (English) Zbl 1089.92043 Math. Biosci. 200, No. 2, 152-169 (2006). MSC: 92D30 92C60 34C23 37N25 PDFBibTeX XMLCite \textit{R. Casagrandi} et al., Math. Biosci. 200, No. 2, 152--169 (2006; Zbl 1089.92043) Full Text: DOI
Itovich, Griselda R.; Moiola, Jorge L. On period doubling bifurcations of cycles and the harmonic balance method. (English) Zbl 1083.37041 Chaos Solitons Fractals 27, No. 3, 647-665 (2006). MSC: 37G15 34C23 PDFBibTeX XMLCite \textit{G. R. Itovich} and \textit{J. L. Moiola}, Chaos Solitons Fractals 27, No. 3, 647--665 (2006; Zbl 1083.37041) Full Text: DOI
Kooi, B. W.; Kuijper, L. D. J.; Kooijman, S. A. L. M. Consequences of symbiosis for food web dynamics. (English) Zbl 1067.92057 J. Math. Biol. 49, No. 3, 227-271 (2004). MSC: 92D40 34C60 37N25 PDFBibTeX XMLCite \textit{B. W. Kooi} et al., J. Math. Biol. 49, No. 3, 227--271 (2004; Zbl 1067.92057) Full Text: DOI
Dhooge, A.; Govaerts, W.; Kuznetsov, Yu. A. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. (English) Zbl 1070.65574 ACM Trans. Math. Softw. 29, No. 2, 141-164 (2003). MSC: 65P30 65Y15 37-04 37M20 37G15 PDFBibTeX XMLCite \textit{A. Dhooge} et al., ACM Trans. Math. Softw. 29, No. 2, 141--164 (2003; Zbl 1070.65574) Full Text: DOI
Jansen, Vincent A. A. The dynamics of two diffusively coupled predator–prey populations. (English) Zbl 1036.92034 Theor. Popul. Biol. 59, No. 2, 119-131 (2001). MSC: 92D40 37N25 PDFBibTeX XMLCite \textit{V. A. A. Jansen}, Theor. Popul. Biol. 59, No. 2, 119--131 (2001; Zbl 1036.92034) Full Text: DOI
Berns, Daniel W.; Moiola, Jorge L.; Chen, Guanrong Detecting period-doubling bifurcation: an approximate monodromy matrix approach. (English) Zbl 1056.93550 Automatica 37, No. 11, 1787-1795 (2001). MSC: 93C10 37N35 34C23 93B52 PDFBibTeX XMLCite \textit{D. W. Berns} et al., Automatica 37, No. 11, 1787--1795 (2001; Zbl 1056.93550) Full Text: DOI
Edwards, Andrew M.; Bees, Martin A. Generic dynamics of a simple plankton population model with a non-integer exponent of closure. (English) Zbl 0977.92027 Chaos Solitons Fractals 12, No. 2, 289-300 (2001). MSC: 92D40 37N25 PDFBibTeX XMLCite \textit{A. M. Edwards} and \textit{M. A. Bees}, Chaos Solitons Fractals 12, No. 2, 289--300 (2001; Zbl 0977.92027) Full Text: DOI
Chen, Guanrong; Moiola, Jorge L.; Wang, Hua O. Bifurcation control: theories, methods, and applications. (English) Zbl 1090.37552 Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, No. 3, 511-548 (2000). MSC: 37G99 34C23 34H05 93C10 PDFBibTeX XMLCite \textit{G. Chen} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, No. 3, 511--548 (2000; Zbl 1090.37552) Full Text: DOI
Govaerts, Willy J. F. Numerical methods for bifurcations of dynamical equilibria. (English) Zbl 0935.37054 Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). xxii, 362 p. (2000). Reviewer: Boris V.Loginov (Ul’yanovsk) MSC: 37M20 65P30 37-02 65-02 PDFBibTeX XMLCite \textit{W. J. F. Govaerts}, Numerical methods for bifurcations of dynamical equilibria. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2000; Zbl 0935.37054) Full Text: DOI
Moiola, Jorge L.; Chua, Leon O. Hopf bifurcations and degeneracies in Chua’s circuit. – A perspective from a frequency domain approach. (English) Zbl 0937.37028 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 1, 295-303 (1999). MSC: 37G15 37G10 37N35 PDFBibTeX XMLCite \textit{J. L. Moiola} and \textit{L. O. Chua}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 1, 295--303 (1999; Zbl 0937.37028) Full Text: DOI
Eirola, Timo Detection of generic one parameter bifurcations of Hamiltonian equilibria. (English) Zbl 0989.37043 Appl. Numer. Math. 29, No. 1, 129-143 (1999). Reviewer: Lev Lerman (Nizhny Novgorod) MSC: 37G10 37J05 34C23 PDFBibTeX XMLCite \textit{T. Eirola}, Appl. Numer. Math. 29, No. 1, 129--143 (1999; Zbl 0989.37043) Full Text: DOI
Govaerts, W.; Kuznetsov, Yu. A.; Sijnave, B. Implementation of Hopf and double-Hopf continuation using bordering methods. (English) Zbl 0934.65140 ACM Trans. Math. Softw. 24, No. 4, 418-436 (1998). MSC: 65P30 37M20 PDFBibTeX XMLCite \textit{W. Govaerts} et al., ACM Trans. Math. Softw. 24, No. 4, 418--436 (1998; Zbl 0934.65140) Full Text: DOI
Kooi, B. W.; Boer, M. P.; Kooijman, S. A. L. M. Consequences of population models for the dynamics of food chains. (English) Zbl 0939.92034 Math. Biosci. 153, No. 2, 99-124 (1998). MSC: 92D40 34C23 37N25 PDFBibTeX XMLCite \textit{B. W. Kooi} et al., Math. Biosci. 153, No. 2, 99--124 (1998; Zbl 0939.92034) Full Text: DOI
Boer, M. P.; Kooi, B. W.; Kooijman, S. A. L. M. Food chain dynamics in the chemostat. (English) Zbl 0938.92029 Math. Biosci. 150, No. 1, 43-62 (1998). MSC: 92D40 37N25 34C05 34C23 PDFBibTeX XMLCite \textit{M. P. Boer} et al., Math. Biosci. 150, No. 1, 43--62 (1998; Zbl 0938.92029) Full Text: DOI
De Vries, Gerda; Sherman, Arthur; Zhu, Hsiu-Rong Diffusively coupled bursters: Effects of cell heterogeneity. (English) Zbl 0942.92010 Bull. Math. Biol. 60, No. 6, 1167-1200 (1998); erratum ibid. 61, No. 5, 1017 (1999). MSC: 92C37 92C30 34C23 37N25 PDFBibTeX XMLCite \textit{G. De Vries} et al., Bull. Math. Biol. 60, No. 6, 1167--1200 (1998; Zbl 0942.92010) Full Text: DOI
Kooi, W. B.; Boer, M. P.; Kooijman, S. A. L. M. Mass balance equation versus logistic equation in food chains. (English) Zbl 0977.92505 J. Biol. Syst. 5, No. 1, 77-85 (1997). MSC: 92D20 37N25 PDFBibTeX XMLCite \textit{W. B. Kooi} et al., J. Biol. Syst. 5, No. 1, 77--85 (1997; Zbl 0977.92505) Full Text: DOI
Behrens, D. A.; Feichtinger, G.; Prskawetz, A. Complex dynamics and control of arms race. (English) Zbl 0970.91007 Eur. J. Oper. Res. 100, No. 1, 192-215 (1997). MSC: 91A20 91A35 37N40 PDFBibTeX XMLCite \textit{D. A. Behrens} et al., Eur. J. Oper. Res. 100, No. 1, 192--215 (1997; Zbl 0970.91007) Full Text: DOI
Kooi, B. W.; Boer, M. P.; Kooijman, S. A. L. M. Complex dynamic behaviour of autonomous microbial food chains. (English) Zbl 0887.92030 J. Math. Biol. 36, No. 1, 24-40 (1997). MSC: 92D40 37N99 37D45 34C05 PDFBibTeX XMLCite \textit{B. W. Kooi} et al., J. Math. Biol. 36, No. 1, 24--40 (1997; Zbl 0887.92030) Full Text: DOI
Govaerts, W.; Guckenheimer, J.; Khibnik, A. Defining functions for multiple Hopf bifurcations. (English) Zbl 0873.65053 SIAM J. Numer. Anal. 34, No. 3, 1269-1288 (1997). MSC: 65H17 37-XX PDFBibTeX XMLCite \textit{W. Govaerts} et al., SIAM J. Numer. Anal. 34, No. 3, 1269--1288 (1997; Zbl 0873.65053) Full Text: DOI
Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. (English) Zbl 0866.35002 Pitman Research Notes in Mathematics Series. 352. Harlow: Longman. 277 p. (1996). Reviewer: A.Cañada (Granada) MSC: 35-02 34-02 37G99 35B40 00B15 PDFBibTeX XMLCite \textit{G. Dangelmayr} et al., Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Harlow: Longman (1996; Zbl 0866.35002)
Luzyanina, Tatyana; Roose, Dirk Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations. (English) Zbl 0855.65092 J. Comput. Appl. Math. 72, No. 2, 379-392 (1996). Reviewer: P.Chocholatý (Bratislava) MSC: 65L20 34K05 34C23 37G99 65L05 34A34 PDFBibTeX XMLCite \textit{T. Luzyanina} and \textit{D. Roose}, J. Comput. Appl. Math. 72, No. 2, 379--392 (1996; Zbl 0855.65092) Full Text: DOI
Kuznetsov, Yu. A.; Rinaldi, S. Remarks on food chain dynamics. (English) Zbl 0844.92025 Math. Biosci. 134, No. 1, 1-33 (1996). MSC: 92D40 34C23 34C05 34C30 34C37 37N99 PDFBibTeX XMLCite \textit{Yu. A. Kuznetsov} and \textit{S. Rinaldi}, Math. Biosci. 134, No. 1, 1--33 (1996; Zbl 0844.92025) Full Text: DOI Link
Feichtinger, G.; Forst, C. V.; Piccardi, C. A nonlinear dynamical model for the dynastic cycle. (English) Zbl 1080.91572 Chaos Solitons Fractals 7, No. 2, 257-271 (1996). MSC: 91D10 37N40 PDFBibTeX XMLCite \textit{G. Feichtinger} et al., Chaos Solitons Fractals 7, No. 2, 257--271 (1996; Zbl 1080.91572) Full Text: DOI
Feichtinger, Gustav; Hommes, Cars H.; Milik, Alexandra Complex dynamics in a threshold advertising model. (English) Zbl 0806.90072 OR Spektrum 16, No. 2, 101-111 (1994). MSC: 90B60 91B62 37D45 PDFBibTeX XMLCite \textit{G. Feichtinger} et al., OR Spektrum 16, No. 2, 101--111 (1994; Zbl 0806.90072) Full Text: DOI
Khibnik, Alexander I.; Kuznetsov, Yuri A.; Levitin, Victor V.; Nikolaev, Eugene V. Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps. (English) Zbl 0784.34030 Physica D 62, No. 1-4, 360-371 (1993). MSC: 34C23 65J99 37G99 65D30 65L99 68N99 PDFBibTeX XMLCite \textit{A. I. Khibnik} et al., Physica D 62, No. 1--4, 360--371 (1993; Zbl 0784.34030) Full Text: DOI