Wu, Yazhi; Tang, Guangyao; Xiang, Changcheng Dynamics of a class of nonlinear pest-natural enemy discrete model. (English) Zbl 07782109 Math. Methods Appl. Sci. 46, No. 5, 5245-5261 (2023). MSC: 92D45 37G15 PDFBibTeX XMLCite \textit{Y. Wu} et al., Math. Methods Appl. Sci. 46, No. 5, 5245--5261 (2023; Zbl 07782109) Full Text: DOI
Glendinning, Paul A.; Simpson, David J. W. Normal forms, differentiable conjugacies, and elementary bifurcations of maps. (English) Zbl 1521.37049 SIAM J. Appl. Math. 83, No. 2, 816-836 (2023). Reviewer: Zhengdong Du (Chengdu) MSC: 37G05 37G10 37G15 PDFBibTeX XMLCite \textit{P. A. Glendinning} and \textit{D. J. W. Simpson}, SIAM J. Appl. Math. 83, No. 2, 816--836 (2023; Zbl 1521.37049) Full Text: DOI arXiv
Huang, Yu-Jhe; Juang, Jonq; Kuo, Tai-Yi; Liang, Yu-Hao Forward-backward and period doubling bifurcations in a discrete epidemic model with vaccination and limited medical resources. (English) Zbl 1518.92148 J. Math. Biol. 86, No. 5, Paper No. 77, 22 p. (2023). MSC: 92D30 92C60 37G10 PDFBibTeX XMLCite \textit{Y.-J. Huang} et al., J. Math. Biol. 86, No. 5, Paper No. 77, 22 p. (2023; Zbl 1518.92148) Full Text: DOI
Burbanks, Andrew; Osbaldestin, Andrew Existence of the FS-type renormalisation fixed point for unidirectionally-coupled pairs of maps. (English) Zbl 1517.37048 J. Phys. A, Math. Theor. 56, No. 19, Article ID 195202, 17 p. (2023). MSC: 37E20 37G10 37M20 82B28 PDFBibTeX XMLCite \textit{A. Burbanks} and \textit{A. Osbaldestin}, J. Phys. A, Math. Theor. 56, No. 19, Article ID 195202, 17 p. (2023; Zbl 1517.37048) Full Text: DOI
Gaiko, Valery A.; Sterk, Alef E.; Broer, Henk W. Bifurcation analysis of the Topp model. (English) Zbl 07819090 Cerejeiras, Paula (ed.) et al., Current trends in analysis, its applications and computation. Proceedings of the 12th ISAAC congress, Aveiro, Portugal, July 29 – August 3, 2019. Cham: Birkhäuser. Trends Math., 3-9 (2022). MSC: 34C23 37G15 37G35 34C05 34C07 PDFBibTeX XMLCite \textit{V. A. Gaiko} et al., in: Current trends in analysis, its applications and computation. Proceedings of the 12th ISAAC congress, Aveiro, Portugal, July 29 -- August 3, 2019. Cham: Birkhäuser. 3--9 (2022; Zbl 07819090) Full Text: DOI
Gonchenko, Sergey V.; Safonov, Klim A.; Zelentsov, Nikita G. Antisymmetric diffeomorphisms and bifurcations of a double conservative Hénon map. (English) Zbl 1517.37051 Regul. Chaotic Dyn. 27, No. 6, 647-667 (2022). MSC: 37E30 37C05 37G10 37G25 PDFBibTeX XMLCite \textit{S. V. Gonchenko} et al., Regul. Chaotic Dyn. 27, No. 6, 647--667 (2022; Zbl 1517.37051) Full Text: DOI
Alidousti, J.; Eskandari, Z.; Fardi, M.; Asadipour, M. Codimension two bifurcations of discrete Bonhoeffer-van der Pol oscillator model. (English) Zbl 1508.37063 Soft Comput. 25, No. 7, 5261-5276 (2021). MSC: 37G10 37G05 34C15 34C23 PDFBibTeX XMLCite \textit{J. Alidousti} et al., Soft Comput. 25, No. 7, 5261--5276 (2021; Zbl 1508.37063) Full Text: DOI
Zhang, Wei; An, Xinlei; Wang, Hongmei; Qiao, Shuai Bifurcation analysis and Hamiltonian energy control of mHR neuron model. (Chinese. English summary) Zbl 1488.34304 J. Yunnan Univ., Nat. Sci. 43, No. 3, 486-494 (2021). MSC: 34C60 34C23 93C20 34C05 34H10 34H05 PDFBibTeX XMLCite \textit{W. Zhang} et al., J. Yunnan Univ., Nat. Sci. 43, No. 3, 486--494 (2021; Zbl 1488.34304) Full Text: DOI
Zhang, Liang; Han, Qin; Tang, Jiashi Anti-control of the period doubling bifurcation at two periodic point of logistic system. (Chinese. English summary) Zbl 1488.34351 J. Wuhan Univ., Nat. Sci. Ed. 67, No. 2, 199-204 (2021). MSC: 34H20 34A34 34C05 PDFBibTeX XMLCite \textit{L. Zhang} et al., J. Wuhan Univ., Nat. Sci. Ed. 67, No. 2, 199--204 (2021; Zbl 1488.34351) Full Text: DOI
Belykh, Vladimir N.; Barabash, Nikita V.; Belykh, Igor V. Sliding homoclinic bifurcations in a Lorenz-type system: analytic proofs. (English) Zbl 1473.37060 Chaos 31, No. 4, 043117, 17 p. (2021). MSC: 37G10 37G15 37C27 37C29 PDFBibTeX XMLCite \textit{V. N. Belykh} et al., Chaos 31, No. 4, 043117, 17 p. (2021; Zbl 1473.37060) Full Text: DOI
Eskandari, Zohreh; Alidousti, Javad; Ghaziani, Reza Khoshsiar Codimension-one and -two bifurcations of a three-dimensional discrete game model. (English) Zbl 1462.39014 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 2, Article ID 2150023, 16 p. (2021). MSC: 39A28 37G10 37N40 91A25 PDFBibTeX XMLCite \textit{Z. Eskandari} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 2, Article ID 2150023, 16 p. (2021; Zbl 1462.39014) Full Text: DOI
Hosham, Hany A. Nonlinear behavior of a novel switching jerk system. (English) Zbl 1457.34030 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 14, Article ID 2050202, 14 p. (2020). MSC: 34A36 34A34 34C23 34C05 34C28 PDFBibTeX XMLCite \textit{H. A. Hosham}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 14, Article ID 2050202, 14 p. (2020; Zbl 1457.34030) Full Text: DOI
Llibre, Jaume; Messias, Marcelo; de Carvalho Reinol, Alisson Zero-Hopf bifurcations in three-dimensional chaotic systems with one stable equilibrium. (English) Zbl 1465.34054 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 13, Article ID 2050189, 11 p. (2020). Reviewer: Eduard Musafirov (Grodno) MSC: 34C23 34C05 34C25 34C28 34C29 34D45 37D45 PDFBibTeX XMLCite \textit{J. Llibre} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 13, Article ID 2050189, 11 p. (2020; Zbl 1465.34054) Full Text: DOI
Ali, Irfan; Saeed, Umer; Din, Qamar Bifurcation analysis and chaos control in a discrete-time plant quality and larch budmoth interaction model with Ricker equation. (English) Zbl 1431.37074 Math. Methods Appl. Sci. 42, No. 18, 7395-7410 (2019). MSC: 37N35 37G10 34H10 93C55 PDFBibTeX XMLCite \textit{I. Ali} et al., Math. Methods Appl. Sci. 42, No. 18, 7395--7410 (2019; Zbl 1431.37074) Full Text: DOI
He, Dongping; Huang, Wentao; Wang, Qinlong Limit cycle flutter and chaotic motion of two-dimensional airfoil system. (Chinese. English summary) Zbl 1449.34139 J. Guangxi Norm. Univ., Nat. Sci. 37, No. 3, 87-95 (2019). MSC: 34C60 34C23 34C28 34C05 34C45 34D20 PDFBibTeX XMLCite \textit{D. He} et al., J. Guangxi Norm. Univ., Nat. Sci. 37, No. 3, 87--95 (2019; Zbl 1449.34139) Full Text: DOI
Cheng, Lifang; Wei, Xiukun; Cao, Hongjun Two-parameter bifurcation analysis of limit cycles of a simplified railway wheelset model. (English) Zbl 1398.34053 Nonlinear Dyn. 93, No. 4, 2415-2431 (2018). MSC: 34C23 37G10 34C05 PDFBibTeX XMLCite \textit{L. Cheng} et al., Nonlinear Dyn. 93, No. 4, 2415--2431 (2018; Zbl 1398.34053) Full Text: DOI
Layek, G. C.; Pati, N. C. Bifurcations and hyperchaos in magnetoconvection of non-Newtonian fluids. (English) Zbl 1402.34049 Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 10, Article ID 1830034, 23 p. (2018). MSC: 34C60 76W05 34C23 34C28 34C05 34C37 PDFBibTeX XMLCite \textit{G. C. Layek} and \textit{N. C. Pati}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 10, Article ID 1830034, 23 p. (2018; Zbl 1402.34049) Full Text: DOI
Du, Zhengdong Periodic orbits in two classes of piecewise smooth maps with positive nonlinear parts. (English) Zbl 1474.37039 J. Appl. Anal. Comput. 7, No. 1, 189-206 (2017). MSC: 37E05 37G05 37G10 PDFBibTeX XMLCite \textit{Z. Du}, J. Appl. Anal. Comput. 7, No. 1, 189--206 (2017; Zbl 1474.37039) Full Text: DOI
Yin, Shan; Shen, Yongkang; Wen, Guilin; Xu, Huidong Analytical determination for degenerate grazing bifurcation points in the single-degree-of-freedom impact oscillator. (English) Zbl 1390.34110 Nonlinear Dyn. 90, No. 1, 443-456 (2017). MSC: 34C23 37G10 PDFBibTeX XMLCite \textit{S. Yin} et al., Nonlinear Dyn. 90, No. 1, 443--456 (2017; Zbl 1390.34110) Full Text: DOI
Ren, Jingli; Yu, Liping; Siegmund, Stefan Bifurcations and chaos in a discrete predator-prey model with Crowley-Martin functional response. (English) Zbl 1390.37084 Nonlinear Dyn. 90, No. 1, 19-41 (2017). MSC: 37G10 92D25 37N25 39A28 37M20 34H10 PDFBibTeX XMLCite \textit{J. Ren} et al., Nonlinear Dyn. 90, No. 1, 19--41 (2017; Zbl 1390.37084) Full Text: DOI
Azimi, Sepinoud; Panchal, Charmi; Mizera, Andrzej; Petre, Ion Multi-stability, limit cycles, and period-doubling bifurcation with reaction systems. (English) Zbl 1387.37043 Int. J. Found. Comput. Sci. 28, No. 8, 1007-1020 (2017). MSC: 37G10 74F25 PDFBibTeX XMLCite \textit{S. Azimi} et al., Int. J. Found. Comput. Sci. 28, No. 8, 1007--1020 (2017; Zbl 1387.37043) Full Text: DOI
Zhang, Hao; Luo, Pengcheng; Ding, Huifang Bifurcation analysis of charged particles moving on a rough surface under different damping effects. (English) Zbl 1367.37047 Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 5, Article ID 1750069, 16 p. (2017). MSC: 37G15 37E30 37N05 37G10 37C75 PDFBibTeX XMLCite \textit{H. Zhang} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 5, Article ID 1750069, 16 p. (2017; Zbl 1367.37047) Full Text: DOI
Chen, Zhi-Min Low-index equilibrium and multiple period-doubling cascades to chaos of atmospheric flow in beta-plane channel. (English) Zbl 1345.34083 Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 8, Article ID 1630020, 16 p. (2016). MSC: 34C60 86A10 34C23 34C05 34C28 34D45 PDFBibTeX XMLCite \textit{Z.-M. Chen}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 8, Article ID 1630020, 16 p. (2016; Zbl 1345.34083) Full Text: DOI
Wolkowicz, Gail S. K.; Yuan, Yuan Effect of light on the growth of non-nitrogen-fixing and nitrogen-fixing phytoplankton in an aquatic system. (English) Zbl 1341.34055 J. Math. Biol. 72, No. 6, 1663-1692 (2016). MSC: 34C60 34D20 34D05 92D25 34C23 34C05 34C28 PDFBibTeX XMLCite \textit{G. S. K. Wolkowicz} and \textit{Y. Yuan}, J. Math. Biol. 72, No. 6, 1663--1692 (2016; Zbl 1341.34055) Full Text: DOI
Colacchio, Giorgio Transitions to chaos in a seven-equation model of the business cycle with income redistribution and private debt. (English) Zbl 1334.34098 Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 2, Article ID 1650027, 22 p. (2016). MSC: 34C60 34C05 34D20 34C23 34C28 PDFBibTeX XMLCite \textit{G. Colacchio}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 2, Article ID 1650027, 22 p. (2016; Zbl 1334.34098) Full Text: DOI
Zhang, Hao; Wang, Xing-Yuan; Lin, Xiao-Hui Chaos and bifurcations in chaotic maps with parameter \(q\): numerical and analytical studies. (English) Zbl 1417.37176 Nonlinear Anal., Model. Control 20, No. 2, 249-262 (2015). MSC: 37G10 39A28 39A33 26A33 PDFBibTeX XMLCite \textit{H. Zhang} et al., Nonlinear Anal., Model. Control 20, No. 2, 249--262 (2015; Zbl 1417.37176) Full Text: DOI
Hadeler, Karl P. Quiescent phases and stability in discrete time dynamical systems. (English) Zbl 1330.37049 Discrete Contin. Dyn. Syst., Ser. B 20, No. 1, 129-152 (2015). MSC: 37G10 37C75 37G35 92D40 37N25 92D25 PDFBibTeX XMLCite \textit{K. P. Hadeler}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 1, 129--152 (2015; Zbl 1330.37049) Full Text: DOI
Simpson, D. J. W. On the relative coexistence of fixed points and period-two solutions near border-collision bifurcations. (English) Zbl 1314.37035 Appl. Math. Lett. 38, 162-167 (2014). MSC: 37G10 PDFBibTeX XMLCite \textit{D. J. W. Simpson}, Appl. Math. Lett. 38, 162--167 (2014; Zbl 1314.37035) Full Text: DOI arXiv
Liang, Hongtao; Tang, Yanxia; Li, Li; Wei, Zhouchao; Wang, Zhen Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system. (English) Zbl 1290.34050 Kybernetika 49, No. 6, 935-947 (2013). MSC: 34C28 34A34 34C23 34C05 PDFBibTeX XMLCite \textit{H. Liang} et al., Kybernetika 49, No. 6, 935--947 (2013; Zbl 1290.34050) Full Text: Link
Ma, Jiying; Xiao, Dongmei Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells. (English) Zbl 1305.92030 Discrete Contin. Dyn. Syst., Ser. B 18, No. 9, 2377-2396 (2013). MSC: 92C37 92C40 37N25 37E05 37G10 PDFBibTeX XMLCite \textit{J. Ma} and \textit{D. Xiao}, Discrete Contin. Dyn. Syst., Ser. B 18, No. 9, 2377--2396 (2013; Zbl 1305.92030) Full Text: DOI
Yamaguchi, Yoshihiro; Tanikawa, Kiyotaka Nonsymmetric saddle-node pairs for the reversible Smale horseshoe map. (English) Zbl 1251.37016 Prog. Theor. Phys. 128, No. 1, 15-30 (2012). MSC: 37B10 37C25 37G15 37E30 PDFBibTeX XMLCite \textit{Y. Yamaguchi} and \textit{K. Tanikawa}, Prog. Theor. Phys. 128, No. 1, 15--30 (2012; Zbl 1251.37016) Full Text: DOI
Foster, Andrew; Khumalo, Melusi Transformation of local bifurcations under collocation methods. (English) Zbl 1230.65137 J. Korean Math. Soc. 48, No. 6, 1101-1123 (2011). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65P30 65L60 65L20 65L06 37N30 37M20 37G10 PDFBibTeX XMLCite \textit{A. Foster} and \textit{M. Khumalo}, J. Korean Math. Soc. 48, No. 6, 1101--1123 (2011; Zbl 1230.65137) Full Text: DOI
Luo, Albert C. J. A Ying-Yang theory in nonlinear discrete dynamical systems. (English) Zbl 1193.37024 Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 4, 1085-1098 (2010). MSC: 37C05 37C25 37G99 PDFBibTeX XMLCite \textit{A. C. J. Luo}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 4, 1085--1098 (2010; Zbl 1193.37024) Full Text: DOI
Leung, A. Y. T.; Guo, Z.; Fung, T. C. The multi-parameter homotopy harmonic balance method for steady state problems. (English) Zbl 1191.65086 Int. J. Comput. Math. 87, No. 5, 1158-1177 (2010). MSC: 65L05 65H20 34A34 65P20 65P30 37G10 PDFBibTeX XMLCite \textit{A. Y. T. Leung} et al., Int. J. Comput. Math. 87, No. 5, 1158--1177 (2010; Zbl 1191.65086) Full Text: DOI
Liu, Xuanliang; Liu, Yongqi; Meng, Xiaoying Existence of periodic solutions to a perturbed four-dimensional system. (English) Zbl 1199.34188 Ann. Differ. Equations 25, No. 1, 46-53 (2009). MSC: 34C23 37G15 34C05 PDFBibTeX XMLCite \textit{X. Liu} et al., Ann. Differ. Equations 25, No. 1, 46--53 (2009; Zbl 1199.34188)
San Martín, Jesús Intermittency cascade. (English) Zbl 1138.37030 Chaos Solitons Fractals 32, No. 2, 816-831 (2007). MSC: 37G10 37D45 37E05 37G15 37N20 37B10 PDFBibTeX XMLCite \textit{J. San Martín}, Chaos Solitons Fractals 32, No. 2, 816--831 (2007; Zbl 1138.37030) Full Text: DOI
Shi, Yuming; Yu, Pei On chaos of the logistic maps. (English) Zbl 1130.37019 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 14, No. 2, 175-195 (2007). MSC: 37D45 37E05 37C70 37C25 37G15 PDFBibTeX XMLCite \textit{Y. Shi} and \textit{P. Yu}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 14, No. 2, 175--195 (2007; Zbl 1130.37019)
Zhao, Wenli; Zhou, Xiaojun Bifurcation and chaos of impact vibration system with two degrees of freedom and clearance. (Chinese. English summary) Zbl 1104.37306 J. Zhejiang Univ., Eng. Sci. 40, No. 8, 1435-1438 (2006). MSC: 37N99 37D45 37G40 37C25 PDFBibTeX XMLCite \textit{W. Zhao} and \textit{X. Zhou}, J. Zhejiang Univ., Eng. Sci. 40, No. 8, 1435--1438 (2006; Zbl 1104.37306)
Stoop, Ruedi; Steeb, Willi-Hans Computable chaos in dynamical systems. (Berechenbares Chaos in dynamischen Systemen.) (German) Zbl 1096.65128 Basel: Birkhäuser (ISBN 3-7643-7550-7/pbk). xii, 264 p. (2006). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 65P20 37D45 65P10 65P30 65P40 65-02 37-02 37M20 37M25 PDFBibTeX XMLCite \textit{R. Stoop} and \textit{W.-H. Steeb}, Berechenbares Chaos in dynamischen Systemen. Basel: Birkhäuser (2006; Zbl 1096.65128)
Jing, Zhujun; Yang, Jianping Bifurcation and chaos in discrete-time predator-prey system. (English) Zbl 1085.92045 Chaos Solitons Fractals 27, No. 1, 259-277 (2006). Reviewer: Josef Hainzl (Freiburg) MSC: 92D40 37N25 37D45 92D25 37C25 37G10 37E99 PDFBibTeX XMLCite \textit{Z. Jing} and \textit{J. Yang}, Chaos Solitons Fractals 27, No. 1, 259--277 (2006; Zbl 1085.92045) Full Text: DOI
Kuznetsov, S. P.; Kuznetsov, A. P.; Sataev, I. R. Multiparameter critical situations, universality and scaling in two-dimensional period-doubling maps. (English) Zbl 1127.37037 J. Stat. Phys. 121, No. 5-6, 697-748 (2005). MSC: 37E20 37J10 37J20 82B28 PDFBibTeX XMLCite \textit{S. P. Kuznetsov} et al., J. Stat. Phys. 121, No. 5--6, 697--748 (2005; Zbl 1127.37037) Full Text: DOI
Killough, D. B.; Edwards, R. Bifurcations in Glass networks. (English) Zbl 1082.37073 Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 2, 395-423 (2005). MSC: 37N99 37N25 37D45 37G40 37C25 PDFBibTeX XMLCite \textit{D. B. Killough} and \textit{R. Edwards}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 2, 395--423 (2005; Zbl 1082.37073) Full Text: DOI
Moghadas, S. M.; Alexander, M. E. Dynamics of a generalized Gause-type predator-prey model with a seasonal functional response. (English) Zbl 1058.92049 Chaos Solitons Fractals 23, No. 1, 55-65 (2005). MSC: 92D40 37N25 34C60 34D05 34D23 34C23 34C25 PDFBibTeX XMLCite \textit{S. M. Moghadas} and \textit{M. E. Alexander}, Chaos Solitons Fractals 23, No. 1, 55--65 (2005; Zbl 1058.92049) Full Text: DOI
Robbio, Federico I.; Alonso, Diego M.; Moiola, Jorge L. Detection of limit cycle bifurcations using harmonic balance methods. (English) Zbl 1066.34035 Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 10, 3647-3654 (2004). MSC: 34C23 37G15 34C05 PDFBibTeX XMLCite \textit{F. I. Robbio} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 10, 3647--3654 (2004; Zbl 1066.34035) Full Text: DOI
Robbio, Federico I.; Alonso, Diego M.; Moiola, Jorge L. On semi-analytical procedure for detecting limit cycle bifurcations. (English) Zbl 1069.34005 Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 3, 951-970 (2004). Reviewer: John Pryce (Swindon) MSC: 34A45 37G15 34C23 34C05 PDFBibTeX XMLCite \textit{F. I. Robbio} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 3, 951--970 (2004; Zbl 1069.34005) Full Text: DOI
Impram, Serkan T.; Johnson, Russell; Pavani, Raffaella On the structure of the solutions of a two-parameter family of three-dimensional ordinary differential equations. (English) Zbl 1056.37068 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 5, 1287-1298 (2003). MSC: 37G20 34C23 PDFBibTeX XMLCite \textit{S. T. Impram} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 5, 1287--1298 (2003; Zbl 1056.37068) Full Text: DOI
D’Amico, María Belén; Moiola, Jorge L.; Paolini, Eduardo E. Controlling bifurcations in maps via a frequency-domain approach. (English) Zbl 1030.93019 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 10, No. 6, 781-798 (2003). Reviewer: Georgy Osipenko (St.Peterburg) MSC: 93C10 93C55 93B52 93C80 37C25 37G10 PDFBibTeX XMLCite \textit{M. B. D'Amico} et al., Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 10, No. 6, 781--798 (2003; Zbl 1030.93019)
Devaney, Robert L. An introduction to chaotic dynamical systems. Reprint of the 2nd (1989) ed. (English) Zbl 1025.37001 Studies in Nonlinearity. Boulder, CO: Westview Press. xvi, 335 p. (2003). MSC: 37-01 37D45 PDFBibTeX XMLCite \textit{R. L. Devaney}, An introduction to chaotic dynamical systems. Reprint of the 2nd (1989) ed. Boulder, CO: Westview Press (2003; Zbl 1025.37001)
Kuznetsov, Alexander P.; Kuznetsov, Sergey P.; Mosekilde, Erik; Turukina, Ludmila V. Two-parameter analysis of the scaling behavior at the onset of chaos: tricritical and pseudo-tricritical points. (English) Zbl 0973.37031 Physica A 300, No. 3-4, 367-385 (2001). MSC: 37H20 PDFBibTeX XMLCite \textit{A. P. Kuznetsov} et al., Physica A 300, No. 3--4, 367--385 (2001; Zbl 0973.37031) Full Text: DOI
Homburg, Ale Jan; Young, Todd Universal scalings in homoclinic doubling cascades. (English) Zbl 0987.37043 Commun. Math. Phys. 222, No. 2, 269-292 (2001). Reviewer: Eugene Ershov (St.Peterburg) MSC: 37G20 37E20 37E05 PDFBibTeX XMLCite \textit{A. J. Homburg} and \textit{T. Young}, Commun. Math. Phys. 222, No. 2, 269--292 (2001; Zbl 0987.37043) Full Text: DOI
Pisarchik, A. N.; Corbalán, R. Shift of attractor boundaries in a system with a slow harmonic parameter perturbation. (English) Zbl 0986.34035 Physica D 150, No. 1-2, 14-24 (2001). MSC: 34C23 37G10 34C28 34D45 34D10 PDFBibTeX XMLCite \textit{A. N. Pisarchik} and \textit{R. Corbalán}, Physica D 150, No. 1--2, 14--24 (2001; Zbl 0986.34035) Full Text: DOI
Davies, Huw G. Sinusoidally varying period-doubling bifurcations. (English) Zbl 0999.37032 Moon, Francis C. (ed.), IUTAM symposium on new applications of nonlinear and chaotic dynamics in mechanics. Proceedings of the IUTAM symposium held in Ithaca, NY, USA, July 27-August 1, 1997. Dordrecht: Kluwer Academic Publishers. Solid Mech. Appl. 63, 23-29 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37G10 37M20 PDFBibTeX XMLCite \textit{H. G. Davies}, Solid Mech. Appl. 63, 23--29 (1999; Zbl 0999.37032)
Matsumura, A. Bifurcation phenomena for the Duffing equation. (English) Zbl 0923.34037 Kawashima, S. (ed.) et al., Advances in nonlinear partial differential equations and stochastics. Proceedings of the conference, Nara Women’s University, Japan, September 21–22, 1996. Dedicated to Professor Yasushi Shizuta on the occasion of his 60th birthday. Singapore: World Scientific. Ser. Adv. Math. Appl. Sci. 48, 292-318 (1998). Reviewer: J.Hainzl (Freiburg) MSC: 34C23 34C25 PDFBibTeX XMLCite \textit{A. Matsumura}, Ser. Adv. Math. Appl. Sci. 48, 292--318 (1998; Zbl 0923.34037)
Kuznetsov, A. P.; Kuznetsov, S. P.; Sataev, I. R. Codimension and typicality in the context of description of transmission to chaos via period-doubling in dissipative dynamical systems. (Russian. English summary) Zbl 1004.37503 Regul. Khaoticheskaya Din. 2, No. 3-4, 90-105 (1997). Reviewer: Messoud Efendiev (Berlin) MSC: 37D45 37E20 37G10 37E05 PDFBibTeX XMLCite \textit{A. P. Kuznetsov} et al., Regul. Khaoticheskaya Din. 2, No. 3--4, 90--105 (1997; Zbl 1004.37503)
Schleiff, Stefan; Schwetlick, Hubert Characterization and computation of period doubling points by minimally extended systems. (English) Zbl 0929.37011 Optim. Methods Softw. 8, No. 1, 1-24 (1997). Reviewer: Alois Klíč (Praha) MSC: 37E15 37E20 37M20 65H17 PDFBibTeX XMLCite \textit{S. Schleiff} and \textit{H. Schwetlick}, Optim. Methods Softw. 8, No. 1, 1--24 (1997; Zbl 0929.37011) Full Text: DOI
Duchesne, Laurent Using characteristic multiplier loci to predict bifurcation phenomena and chaos – a tutorial. (English) Zbl 0844.58065 IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 40, No. 10, 683-688 (1993). MSC: 37G99 34C05 PDFBibTeX XMLCite \textit{L. Duchesne}, IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 40, No. 10, 683--688 (1993; Zbl 0844.58065) Full Text: DOI
Aston, P. J. Understanding the global solutions of the capillary-gravity wave problem. (English) Zbl 0778.76010 Wave Motion 17, No. 2, 113-141 (1993). Reviewer: Y.Kivshar (Düsseldorf) MSC: 76B15 76B45 PDFBibTeX XMLCite \textit{P. J. Aston}, Wave Motion 17, No. 2, 113--141 (1993; Zbl 0778.76010) Full Text: DOI
Tanikawa, Kiyotaka; Yamaguchi, Yoshihiro Stable and unstable manifolds during and after the period-doubling bifurcation in dissipative 2D maps. (English) Zbl 0924.58076 Ushiki, S. (ed.), Proceedings of the RIMS conference on chaotic dynamical systems, Kyoto, Japan, July 7–10, 1992. Singapore: World Scientific. Advanced Series in Dynamical Systems. 13, 36-47 (1993). MSC: 37C25 37G99 PDFBibTeX XMLCite \textit{K. Tanikawa} and \textit{Y. Yamaguchi}, in: Proceedings of the RIMS conference on chaotic dynamical systems, Kyoto, Japan, July 7--10, 1992. Singapore: World Scientific. 36--47 (1993; Zbl 0924.58076)
Komuro, Motomasa Bifurcation equations of continuous piecewise-linear vector fields. (English) Zbl 0765.58021 Japan J. Ind. Appl. Math. 9, No. 2, 269-312 (1992). Reviewer: L.Maxim-Răileanu (Iaşi) MSC: 37G99 34C23 PDFBibTeX XMLCite \textit{M. Komuro}, Japan J. Ind. Appl. Math. 9, No. 2, 269--312 (1992; Zbl 0765.58021) Full Text: DOI
Feudel, Ulrike; Jansen, Wolfgang CANDYS/QA – a software system for qualitative analysis of nonlinear dynamical systems. (English) Zbl 0872.65059 Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, No. 4, 773-794 (1992). MSC: 65L05 34-04 34A34 34C23 37-XX 65Y15 PDFBibTeX XMLCite \textit{U. Feudel} and \textit{W. Jansen}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, No. 4, 773--794 (1992; Zbl 0872.65059) Full Text: DOI
Nolte, Klaus-Georg Universal appearance of periodic orbits in the Lorenz equations. (English) Zbl 0749.34025 C. R. Math. Acad. Sci., Soc. R. Can. 13, No. 4, 125-130 (1991). MSC: 34C25 34C05 34D45 37G99 PDFBibTeX XMLCite \textit{K.-G. Nolte}, C. R. Math. Acad. Sci., Soc. R. Can. 13, No. 4, 125--130 (1991; Zbl 0749.34025)
Drazin, Philip G. Stability of non-parallel flow in a channel. (English) Zbl 0756.76029 Matematiche 46, No. 1, 137-146 (1991). MSC: 76E99 76D05 76-02 PDFBibTeX XMLCite \textit{P. G. Drazin}, Matematiche 46, No. 1, 137--146 (1991; Zbl 0756.76029)
Yamamoto, Norio Singular points of plane curves generated by period doubling bifurcation points and a method for computing them. (English) Zbl 0874.58062 Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, No. 4, 795-802 (1991). MSC: 37G99 34C15 65H10 34C23 PDFBibTeX XMLCite \textit{N. Yamamoto}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, No. 4, 795--802 (1991; Zbl 0874.58062) Full Text: DOI
Raouf, Raouf A.; Nayfeh, Ali H. Nonlinear axisymmetric response of closed spherical shells to a radial harmonic excitation. (English) Zbl 0729.73114 Int. J. Non-Linear Mech. 25, No. 5, 475-492 (1990). MSC: 74H45 74S30 74G60 74K15 74P10 65D05 34C05 34C23 PDFBibTeX XMLCite \textit{R. A. Raouf} and \textit{A. H. Nayfeh}, Int. J. Non-Linear Mech. 25, No. 5, 475--492 (1990; Zbl 0729.73114) Full Text: DOI
Devaney, Robert L. An introduction to chaotic dynamical systems. 2nd ed. (English) Zbl 0695.58002 Redwood City, CA etc.: Addison-Wesley Publishing Company, Inc. xvi, 336 p. (1989). MSC: 37-01 37Dxx 37D45 37G99 PDFBibTeX XMLCite \textit{R. L. Devaney}, An introduction to chaotic dynamical systems. 2nd ed. Redwood City, CA etc.: Addison-Wesley Publishing Company, Inc. (1989; Zbl 0695.58002)
Janssen, H.; Van Dooren, R. A one-step integration routine for normal differential systems, based on Gauss-Legendre quadrature. (English) Zbl 0683.65051 J. Comput. Appl. Math. 28, 207-217 (1989). Reviewer: M.Calvo MSC: 65L05 65L50 65L20 34A34 PDFBibTeX XMLCite \textit{H. Janssen} and \textit{R. Van Dooren}, J. Comput. Appl. Math. 28, 207--217 (1989; Zbl 0683.65051) Full Text: DOI
Ling, Fuhua A multiple shooting method for determining periodic windows of one- dimensional maps. (English) Zbl 0682.65081 Chin. Sci. Bull. 34, No. 6, 462-467 (1989). Reviewer: M.Sablik MSC: 65Q05 PDFBibTeX XMLCite \textit{F. Ling}, Chin. Sci. Bull. 34, No. 6, 462--467 (1989; Zbl 0682.65081)
Chossat, Pascal; Golubitsky, Martin Iterates of maps with symmetry. (English) Zbl 0694.58030 SIAM J. Math. Anal. 19, No. 6, 1259-1270 (1988). Reviewer: Y.Asoo MSC: 37G99 37C55 PDFBibTeX XMLCite \textit{P. Chossat} and \textit{M. Golubitsky}, SIAM J. Math. Anal. 19, No. 6, 1259--1270 (1988; Zbl 0694.58030) Full Text: DOI Link
Kubíček, Milan; Holodniok, Martin Algorithms for determination of period-doubling bifurcation points in ordinary differential equations. (English) Zbl 0622.65069 J. Comput. Phys. 70, 203-217 (1987). Reviewer: Yu.V.Kostarchuk MSC: 65L99 37-XX PDFBibTeX XMLCite \textit{M. Kubíček} and \textit{M. Holodniok}, J. Comput. Phys. 70, 203--217 (1987; Zbl 0622.65069) Full Text: DOI
Siemens, Duane P.; Bucher, Manfred New graphical method for the iteration of one-dimensional maps. (English) Zbl 0652.65037 Physica D 20, 363-373 (1986). MSC: 65H05 65S05 37G99 PDFBibTeX XMLCite \textit{D. P. Siemens} and \textit{M. Bucher}, Physica D 20, 363--373 (1986; Zbl 0652.65037) Full Text: DOI
Devaney, Robert L. An introduction to chaotic dynamical systems. (English) Zbl 0632.58005 Menlo Park, California, etc.: The Benjamin/Cummings Publishing Co., Inc. (Distr. by Addison-Wesley, Amsterdam). XIV, 320 p. (1986). Reviewer: E.D.Belokolos MSC: 37-01 37Dxx 37D45 37G99 PDFBibTeX XML
Alexander, J. C. A period-doubling bubble in the dynamics of two coupled oscillators. (English) Zbl 0591.92014 Nonlinear oscillations in biology and chemistry, Proc. Meet., Salt Lake City/Utah 1985, Lect. Notes Biomath. 66, 208-220 (1986). MSC: 92Cxx 92Exx 34C05 PDFBibTeX XML
Akamatsu, N.; Hannaford, B.; Stark, L. An intrinsic mechanism for the oscillatory contraction of muscle. (English) Zbl 0583.92008 Biol. Cybern. 53, 219-227 (1986). MSC: 92Cxx 92F05 PDFBibTeX XMLCite \textit{N. Akamatsu} et al., Biol. Cybern. 53, 219--227 (1986; Zbl 0583.92008) Full Text: DOI
Miles, John Resonant motion of a spherical pendulum. (English) Zbl 0577.70025 Physica D 11, 309-323 (1984). MSC: 70K40 34C15 70K30 PDFBibTeX XMLCite \textit{J. Miles}, Physica D 11, 309--323 (1984; Zbl 0577.70025) Full Text: DOI
Holodniok, Martin; Kubíček, Milan Computation of period doubling bifurcation points in ordinary differential equations. (English) Zbl 0577.65074 TUM, Inst. Math. TUM-M8406, 21 p (1984). Reviewer: J.Oliver MSC: 65L15 34L99 PDFBibTeX XML
Keller, Herbert B. The bordering algorithm and path following near singular points of higher nullity. (English) Zbl 0536.65017 SIAM J. Sci. Stat. Comput. 4, 573-582 (1983). Reviewer: B.Kearfott MSC: 65F05 65H10 65L10 PDFBibTeX XMLCite \textit{H. B. Keller}, SIAM J. Sci. Stat. Comput. 4, 573--582 (1983; Zbl 0536.65017) Full Text: DOI Link
Klič, Alois Period doubling bifurcations in a two-box model of the brusselator. (English) Zbl 0531.34030 Apl. Mat. 28, 335-343 (1983). MSC: 34C25 34C05 37G99 37N99 PDFBibTeX XMLCite \textit{A. Klič}, Apl. Mat. 28, 335--343 (1983; Zbl 0531.34030) Full Text: EuDML
Sparrow, Colin The Lorenz equations: bifurcations, chaos, and strange attractors. (English) Zbl 0504.58001 Applied Mathematical Sciences, 41. New York - Heidelberg Berlin: Springer-Verlag. XII, 269 p. DM 54.00; $ 21.60 (1982). MSC: 37-02 37G99 37D45 37C25 PDFBibTeX XML
Lanford, Oscar E. III A computer-assisted proof of the Feigenbaum conjectures. (English) Zbl 0487.58017 Bull. Am. Math. Soc., New Ser. 6, 427-434 (1982). MSC: 37G99 37C25 54H20 PDFBibTeX XMLCite \textit{O. E. Lanford III}, Bull. Am. Math. Soc., New Ser. 6, 427--434 (1982; Zbl 0487.58017) Full Text: DOI
Mallet-Paret, John; Yorke, James A. Snakes: oriented families of periodic orbits, their sources, sinks, and continuation. (English) Zbl 0487.34038 J. Differ. Equations 43, 419-450 (1982). MSC: 34C25 PDFBibTeX XMLCite \textit{J. Mallet-Paret} and \textit{J. A. Yorke}, J. Differ. Equations 43, 419--450 (1982; Zbl 0487.34038) Full Text: DOI
Devaney, Robert L. Genealogy of periodic points of maps of the interval. (English) Zbl 0472.58017 Trans. Am. Math. Soc. 265, 137-146 (1981). MSC: 37G99 PDFBibTeX XMLCite \textit{R. L. Devaney}, Trans. Am. Math. Soc. 265, 137--146 (1981; Zbl 0472.58017) Full Text: DOI
Mallet-Paret, John; Yorke, James A. Two types of Hopf bifurcation points: Sources and sinks of families of periodic orbits. (English) Zbl 0485.58014 Nonlinear dynamics, int. Conf., New York 1979, Ann. N.Y. Acad. Sci. 357, 300-304 (1980). MSC: 37G99 34C25 PDFBibTeX XML
Collet, P.; Eckmann, J.-P.; Lanford, O. E. Renormalization group analysis of some highly bifurcated families. (English) Zbl 0479.58013 Quantum fields - algebras, processes, Proc. Symp., Bielefeld 1978, 125-134 (1980). MSC: 37D45 37G99 26A18 37C25 54H20 PDFBibTeX XML
Collet, P.; Eckmann, J.-P.; Lanford, O. E. III Universal properties of maps on an interval. (English) Zbl 0455.58024 Commun. Math. Phys. 76, 211-254 (1980). MSC: 37C25 37G99 PDFBibTeX XMLCite \textit{P. Collet} et al., Commun. Math. Phys. 76, 211--254 (1980; Zbl 0455.58024) Full Text: DOI