Karatetskaia, Efrosiniia; Koryakin, Vladislav; Soldatkin, Konstantin; Kazakov, Alexey Routes to chaos in a three-dimensional cancer model. (English) Zbl 07955947 Regul. Chaotic Dyn. 29, No. 5, 777-793 (2024). MSC: 37C29 37G35 37N25 × Cite Format Result Cite Review PDF Full Text: DOI
Hinsley, Carter; Scully, James; Shilnikov, Andrey L. Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus. (English) Zbl 1545.37045 Ukr. Math. J. 75, No. 12, 1822-1840 (2024) and Ukr. Mat. Zh. 75, No. 12, 1608-1626 (2023). MSC: 37G10 37G20 37G40 37E05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gonchenko, Sergey (ed.); Kazakov, Alexey (ed.); Turaev, Dmitry (ed.); Shilnikov, Andrey L. (ed.) Leonid Shilnikov and mathematical theory of dynamical chaos. (English) Zbl 07867638 Chaos 32, No. 1, Article ID 010402, 15 p. (2022). MSC: 01A70 37Gxx × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Rodrigues, Alexandre A. P. Unfolding a Bykov attractor: from an attracting torus to strange attractors. (English) Zbl 1498.34155 J. Dyn. Differ. Equations 34, No. 2, 1643-1677 (2022). MSC: 34D45 34C37 37D45 37G35 34C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Xiong; Chen, Guanrong; Clinton Sprott, Julien Chaotic systems with any number and various types of equilibria. (English) Zbl 1506.37049 Wang, Xiong (ed.) et al., Chaotic systems with multistability and hidden attractors. Cham: Springer. Emerg. Complex. Comput. 40, 125-146 (2021). MSC: 37D45 37C75 37C29 34C28 × Cite Format Result Cite Review PDF Full Text: DOI
Rodrigues, Alexandre A. P. Dissecting a resonance wedge on heteroclinic bifurcations. (English) Zbl 1479.34079 J. Stat. Phys. 184, No. 3, Paper No. 25, 32 p. (2021). MSC: 34C40 34C23 34C45 34C37 37D45 34C05 34C20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gonchenko, Sergey; Kazakov, Alexey; Turaev, Dmitry Wild pseudohyperbolic attractor in a four-dimensional Lorenz system. (English) Zbl 1472.34106 Nonlinearity 34, No. 4, 2018-2047 (2021). Reviewer: Eduard Musafirov (Grodno) MSC: 34D45 34A34 34C28 37D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Xianyi; Wang, Haijun A three-dimensional nonlinear system with a single heteroclinic trajectory. (English) Zbl 1457.34069 J. Appl. Anal. Comput. 10, No. 1, 249-266 (2020). MSC: 34C37 34D20 37C29 × Cite Format Result Cite Review PDF Full Text: DOI
Malykh, Semyon; Bakhanova, Yuliya; Kazakov, Alexey; Pusuluri, Krishna; Shilnikov, Andrey Homoclinic chaos in the Rössler model. (English) Zbl 1451.34060 Chaos 30, No. 11, 113126, 18 p. (2020). MSC: 34C60 34C28 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wu, Qiujie; Hong, Qinghui; Liu, Xiaoyang; Wang, Xiaoping; Zeng, Zhigang Constructing multi-butterfly attractors based on sprott C system via non-autonomous approaches. (English) Zbl 1428.37083 Chaos 29, No. 4, 043112, 11 p. (2019). MSC: 37M22 37N35 × Cite Format Result Cite Review PDF Full Text: DOI
Newhouse, Sheldon E. On a differentiable linearization theorem of Philip Hartman. (English) Zbl 1391.37025 Katok, Anatole (ed.) et al., Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2560-9/pbk; 978-1-4704-4119-7/ebook). Contemporary Mathematics 692, 209-262 (2017). Reviewer: Kazuhiro Sakai (Utsunomiya) MSC: 37D10 37C15 37C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Dongchen; Turaev, Dmitry V. Existence of heterodimensional cycles near shilnikov loops in systems with a \(\mathbb{Z}_2\) symmetry. (English) Zbl 1360.37129 Discrete Contin. Dyn. Syst. 37, No. 8, 4399-4437 (2017). MSC: 37G20 37G25 37G35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Dongchen Homoclinic bifurcations that give rise to heterodimensional cycles near a saddle-focus equilibrium. (English) Zbl 1381.37061 Nonlinearity 30, No. 1, 173-206 (2017). Reviewer: Alessandro Calamai (Ancona) MSC: 37G20 37G25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gonchenko, Sergey; Ovsyannikov, Ivan Homoclinic tangencies to resonant saddles and discrete Lorenz attractors. (English) Zbl 1372.37049 Discrete Contin. Dyn. Syst., Ser. S 10, No. 2, 273-288 (2017). Reviewer: Carlo Laing (Auckland) MSC: 37C29 37C70 37G25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gonchenko, A. S.; Gonchenko, S. V. Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps. (English) Zbl 1376.37047 Physica D 337, 43-57 (2016). MSC: 37C05 37D45 39A33 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Labouriau, Isabel S.; Rodrigues, Alexandre A. P. Global bifurcations close to symmetry. (English) Zbl 1364.37115 J. Math. Anal. Appl. 444, No. 1, 648-671 (2016). Reviewer: Maite Grau (Lleida) MSC: 37G20 37G40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Haijun; Li, Xianyi Some new insights into a known Chen-like system. (English) Zbl 1343.34102 Math. Methods Appl. Sci. 39, No. 7, 1747-1764 (2016). MSC: 34C28 34C45 34C37 34D20 34C05 34A34 34E15 34D08 34C23 × Cite Format Result Cite Review PDF Full Text: DOI
Rodrigues, Alexandre A. P. Moduli for heteroclinic connections involving saddle-foci and periodic solutions. (English) Zbl 1366.37052 Discrete Contin. Dyn. Syst. 35, No. 7, 3155-3182 (2015). MSC: 37C29 37C15 37C20 37C27 37C10 37C70 × Cite Format Result Cite Review PDF Full Text: DOI
Labouriau, Isabel S.; Rodrigues, Alexandre A. P. Dense heteroclinic tangencies near a Bykov cycle. (English) Zbl 1326.34078 J. Differ. Equations 259, No. 11, 5875-5902 (2015). MSC: 34C37 34C28 37C29 37D05 37G35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Afraimovich, Valentin S.; Gonchenko, Sergey V.; Lerman, Lev M.; Shilnikov, Andrey L.; Turaev, Dmitry V. Scientific heritage of L. P. Shilnikov. (English) Zbl 1353.37001 Regul. Chaotic Dyn. 19, No. 4, 435-460 (2014). Reviewer: Svitlana P. Rogovchenko (Kristiansand) MSC: 37-02 37C29 37D45 01A65 37G15 × Cite Format Result Cite Review PDF Full Text: DOI
Aguirre, Pablo; Krauskopf, Bernd; Osinga, Hinke M. Global invariant manifolds near a Shilnikov homoclinic bifurcation. (English) Zbl 1309.34077 J. Comput. Dyn. 1, No. 1, 1-38 (2014). MSC: 34C37 34C45 37D45 34C23 37M99 × Cite Format Result Cite Review PDF Full Text: DOI
Gonchenko, Alexander; Gonchenko, Sergey; Kazakov, Alexey; Turaev, Dmitry Simple scenarios of onset of chaos in three-dimensional maps. (English) Zbl 1300.37024 Int. J. Bifurcation Chaos Appl. Sci. Eng. 24, No. 8, Article ID 1440005, 25 p. (2014). MSC: 37D45 37C29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grégoire-Lacoste, François; Jacquemet, Vincent; Vinet, Alain Bifurcations, sustained oscillations and torus bursting involving ionic concentrations dynamics in a canine atrial cell model. (English) Zbl 1315.92007 Math. Biosci. 250, 10-25 (2014). MSC: 92B25 92C40 92C30 × Cite Format Result Cite Review PDF Full Text: DOI
Algaba, Antonio; Merino, Manuel; Rodríguez-Luis, Alejandro J. Analysis of a Belyakov homoclinic connection with \(\mathbb Z_2\)-symmetry. (English) Zbl 1268.37017 Nonlinear Dyn. 69, No. 1-2, 519-529 (2012). MSC: 37C29 37C10 × Cite Format Result Cite Review PDF Full Text: DOI
Barrientos, Pablo G.; Ibáñez, Santiago; Rodríguez, J. Ángel Heteroclinic cycles arising in generic unfoldings of nilpotent singularities. (English) Zbl 1242.34079 J. Dyn. Differ. Equations 23, No. 4, 999-1028 (2011). Reviewer: Eugene Ershov (St. Petersburg) MSC: 34C37 34C23 34C05 34C28 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Drubi, Fátima; Ibáñez, Santiago; Rodríguez, J. Ángel Hopf-pitchfork singularities in coupled systems. (English) Zbl 1220.37042 Physica D 240, No. 9-10, 825-840 (2011). Reviewer: Valery A. Gaiko (Groningen) MSC: 37G35 37G10 × Cite Format Result Cite Review PDF Full Text: DOI
Carmona, Victoriano; Fernández-Sánchez, Fernando; García-Medina, Elisabeth; Teruel, Antonio E. Existence of homoclinic connections in continuous piecewise linear systems. (English) Zbl 1311.34023 Chaos 20, No. 1, 013124, 8 p. (2010). MSC: 34A12 34C37 × Cite Format Result Cite Review PDF Full Text: DOI Link
Driesse, Ramon; Homburg, Ale Jan Resonance bifurcation from homoclinic cycles. (English) Zbl 1170.34031 J. Differ. Equations 246, No. 7, 2681-2705 (2009). Reviewer: Giuseppe Gaeta (Milano) MSC: 34C37 37G40 34C23 × Cite Format Result Cite Review PDF Full Text: DOI
Kolesov, A. Yu.; Rozov, N. Kh. The nature of the bufferness phenomenon in weakly dissipative systems. (English) Zbl 1177.37029 Theor. Math. Phys. 146, No. 3, 376-392 (2006); translation from Teor. Mat. Fiz. 146, No. 3, 447-466 (2006). MSC: 37C70 82C05 × Cite Format Result Cite Review PDF Full Text: DOI
Homburg, Ale Jan; Knobloch, Jürgen Multiple homoclinic orbits in conservative and reversible systems. (English) Zbl 1162.34034 Trans. Am. Math. Soc. 358, No. 4, 1715-1740 (2006). MSC: 34C37 34C14 37C29 × Cite Format Result Cite Review PDF Full Text: DOI
Gonchenko, S. V.; Ovsyannikov, I. I.; Simó, C.; Turaev, D. Three-dimensional Hénon-like maps and wild Lorenz-like attractors. (English) Zbl 1097.37023 Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 11, 3493-3508 (2005). MSC: 37D45 37E99 37D30 37G15 37G35 × Cite Format Result Cite Review PDF Full Text: DOI
Homburg, Ale Jan Singular heteroclinic cycles. (English) Zbl 0954.34031 J. Differ. Equations 161, No. 2, 358-402 (2000). Reviewer: Eugene Ershov (St.Peterburg) MSC: 34C23 37G20 34C37 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Bykov, V. V. On bifurcations leading to chaos in Chua’s circuit. (English) Zbl 0939.34042 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 4-5, 685-699 (1998). MSC: 34C60 37D45 34C28 34C23 × Cite Format Result Cite Review PDF Full Text: DOI
Belykh, V. N.; Bykov, V. V. Bifurcations for heteroclinic orbits of a periodic motion and a saddle-focus and dynamical chaos. (English) Zbl 0934.37037 Chaos Solitons Fractals 9, No. 1-2, 1-18 (1998). MSC: 37D45 37G20 × Cite Format Result Cite Review PDF Full Text: DOI
Bykov, V. V. On bifurcations leading to chaos in Chua’s circuit. (English) Zbl 1109.37304 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 4, 685-699 (1998). MSC: 37G99 37D45 37N35 × Cite Format Result Cite Review PDF Full Text: DOI
Zhu, Deming Exponential trichotomy and heteroclinic bifurcations. (English) Zbl 0877.34037 Nonlinear Anal., Theory Methods Appl. 28, No. 3, 547-557 (1997). Reviewer: M.A.Teixeira (Campinas) MSC: 34C37 37G99 34C23 × Cite Format Result Cite Review PDF Full Text: DOI
Shilnikov, Leonid Mathematical problems of nonlinear dynamics: a tutorial. (English) Zbl 0909.58008 Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, No. 9, 1953-2001 (1997). MSC: 37Cxx 34Cxx 37D15 37D99 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Bykov, V. V. One mechanism of appearance of a spiral quasiattractor involving heteroclinic contours. (English) Zbl 0889.58054 Comput. Math. Appl. 34, No. 2-4, 229-244 (1997). MSC: 37G99 37D45 37D99 × Cite Format Result Cite Review PDF Full Text: DOI
Gonchenko, S. V.; Shil’nikov, L. P.; Sten’kin, O. V.; Turaev, D. V. Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence. (English) Zbl 0889.58055 Comput. Math. Appl. 34, No. 2-4, 111-142 (1997). MSC: 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Mira, Christian Some historical aspects of nonlinear dynamics – possible trends for the future. (English) Zbl 0901.34003 J. Franklin Inst. 334B, No. 5-6, 1075-1113 (1997). MSC: 34-03 70-03 37-XX 01A75 × Cite Format Result Cite Review PDF Full Text: DOI
Shilnikov, Leonid Mathematical problems of nonlinear dynamics: A tutorial. (English) Zbl 0888.58028 J. Franklin Inst. 334B, No. 5-6, 793-864 (1997). MSC: 37D45 93C10 × Cite Format Result Cite Review PDF Full Text: DOI
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits. (English) Zbl 1055.37578 Chaos 6, No. 1, 15-31 (1996). MSC: 37C29 34C37 37D45 37C70 37D25 × Cite Format Result Cite Review PDF Full Text: DOI
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. On models with non-rough Poincaré homoclinic curves. (English) Zbl 0783.58049 Physica D 62, No. 1-4, 1-14 (1993). MSC: 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Blázquez, M.; Tuma, E. Chaos in infinite dimensions: A generalization of a theorem of Šil’nikov. (English) Zbl 0804.34053 Nonlinear Anal., Theory Methods Appl. 21, No. 2, 103-121 (1993). Reviewer: E.Ershov (St.Peterburg) MSC: 34G20 34C37 × Cite Format Result Cite Review PDF Full Text: DOI
Ceballos, J. C.; Labarca, R. A note on modulus of stability for cycles of the complex type. (English) Zbl 0753.58026 Physica D 55, No. 1-2, 37-44 (1992). Reviewer: Ding Tongren (Beijing) MSC: 37A30 37G15 34C37 × Cite Format Result Cite Review PDF Full Text: DOI
Chow, Shui-Nee; Deng, Bo; Fiedler, Bernold Homoclinic bifurcation at resonant eigenvalues. (English) Zbl 0703.34050 J. Dyn. Differ. Equations 2, No. 2, 177-244 (1990). Reviewer: D.Bobrowski MSC: 34C15 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Deng, Bo Exponential expansion with Šil’nikov’s saddle-focus. (English) Zbl 0703.34041 J. Differ. Equations 82, No. 1, 156-173 (1989). Reviewer: D.Bobrowski MSC: 34C05 × Cite Format Result Cite Review PDF Full Text: DOI