Two-parameter bifurcations and global dynamics of asymmetrically excited oscillators with two-sided elastic and rigid constraints
•The differences of the two-parameter existence ranges and evolution laws for periodic and chaotic attractors between two oscillators are discussed.•The boundary and interior characteristics of two types of transient regions are revealed.•Bifurcations induced by the collision between the chaotic/per...
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Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2025-01, Vol.140, p.108419, Article 108419 |
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Sprache: | eng |
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Zusammenfassung: | •The differences of the two-parameter existence ranges and evolution laws for periodic and chaotic attractors between two oscillators are discussed.•The boundary and interior characteristics of two types of transient regions are revealed.•Bifurcations induced by the collision between the chaotic/periodic attractor and an unstable periodic attractor are revealed.•The relationship between bifurcations and evolutions of basins of attraction is revealed.
Asymmetrically excited oscillators with two-sided elastic and rigid constraints are considered, and the global Poincaré mapping structures of all types of periodic attractors are constructed. The numerical procedure of continuation shooting approach is presented for the existence and stability analysis of periodic attractors. By using the direct numerical simulation, shooting approach, cell mapping concept, continuation method and largest Lyapunov exponent (LLE), the differences of the two-parameter existence ranges and evolution laws for periodic and chaotic attractors between two oscillators are discussed, the global dynamics of coexisting attractors is analyzed, and some easily hidden attractors, such as period-doubling-induced saddle-node bifurcation, are attempted to be discovered. Thereby the boundary and interior characteristics of two types of transient regions are revealed in both oscillators, as well as the important roles of unstable periodic attractors in the dynamical evolutions. Under the circumstance of elastic constraints, the grazing-induced bifurcations produce hysteresis and subharmonic inclusion regions. However, the discontinuity grazing bifurcations of period-1 attractor directly generate two types of transient regions under the circumstance of rigid constraints. When an unstable attractor meets a coexisting stable periodic attractor, a saddle-node bifurcation is induced under the circumstance of elastic constraints, while under the circumstance of rigid constraints, a grazing bifurcation can also be induced. Under the circumstance of elastic constraints, an unstable periodic attractor that causes crisis bifurcation is emanated from saddle-node bifurcation, while under the circumstance of rigid constraints, it can be emanated from grazing bifurcation. It should be noted that at the grazing and grazing-induced saddle-node points, the stable attractor is terminated as its basin of attraction reduces to 0. |
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ISSN: | 1007-5704 |
DOI: | 10.1016/j.cnsns.2024.108419 |