“…We have further developed the scenario leading to the chaotic dynamics appearance suggested by Chumakov and Slinko [7]. In addition, we have developed methods for calculation of the periodic solutions with large periods and estimation of the global error of numerical integration (see [12]). …”
Section: Resultsmentioning
confidence: 99%
“…In [12,13] we showed that a highly sensitive dependence on initial conditions appears due to the existence of a tunnel-type bundle of trajectories which is formed by stable and unstable canards. Sensitive dependence on initial conditions means that nearby trajectories separate exponentially fast as time increases.…”
Section: Canards High Parametric Sensitivitymentioning
confidence: 96%
“…The unstable periodic orbits of S u evolve from harmonic to relaxation oscillations as z increases. This happens via canard explosion over a very small range of parameter z since z 0 À z 2 H % 3:8 Á 10 À4 [12]. The unstable periodic orbits of S u emerge from the Andronov-Hopf bifurcation at z ¼ z 2 H , grow explosively in amplitude from the harmonic oscillations of small amplitude (cycle 5 0 ) via the canard-cycles without head (cycles 4 0 , .…”
Section: Canards High Parametric Sensitivitymentioning
confidence: 99%
“…6 presents the chaotic behavior in the phase space of concentrations x, y, and z (a) and the time dependence of z-coordinate (b). To be sure in the computational results, we used some special procedures of higher accuracy with a posteriori estimation of the global error of numerical integration [12].…”
Section: Chaotic Multi-peak Oscillations In Modelmentioning
confidence: 99%
“…The maximal family of periodic orbits of system (9) for k 2 = 8 with the orbits corresponding to the following values of parameter: z = 010), 0.3116 (11), 0.3025(12), and 0.2954(13). The Andronov-Hopf bifurcation also occurs at z 2 H ¼ 0:381826.…”
“…We have further developed the scenario leading to the chaotic dynamics appearance suggested by Chumakov and Slinko [7]. In addition, we have developed methods for calculation of the periodic solutions with large periods and estimation of the global error of numerical integration (see [12]). …”
Section: Resultsmentioning
confidence: 99%
“…In [12,13] we showed that a highly sensitive dependence on initial conditions appears due to the existence of a tunnel-type bundle of trajectories which is formed by stable and unstable canards. Sensitive dependence on initial conditions means that nearby trajectories separate exponentially fast as time increases.…”
Section: Canards High Parametric Sensitivitymentioning
confidence: 96%
“…The unstable periodic orbits of S u evolve from harmonic to relaxation oscillations as z increases. This happens via canard explosion over a very small range of parameter z since z 0 À z 2 H % 3:8 Á 10 À4 [12]. The unstable periodic orbits of S u emerge from the Andronov-Hopf bifurcation at z ¼ z 2 H , grow explosively in amplitude from the harmonic oscillations of small amplitude (cycle 5 0 ) via the canard-cycles without head (cycles 4 0 , .…”
Section: Canards High Parametric Sensitivitymentioning
confidence: 99%
“…6 presents the chaotic behavior in the phase space of concentrations x, y, and z (a) and the time dependence of z-coordinate (b). To be sure in the computational results, we used some special procedures of higher accuracy with a posteriori estimation of the global error of numerical integration [12].…”
Section: Chaotic Multi-peak Oscillations In Modelmentioning
confidence: 99%
“…The maximal family of periodic orbits of system (9) for k 2 = 8 with the orbits corresponding to the following values of parameter: z = 010), 0.3116 (11), 0.3025(12), and 0.2954(13). The Andronov-Hopf bifurcation also occurs at z 2 H ¼ 0:381826.…”
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