Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
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55 citations
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TL;DR: In this paper, the authors performed a systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, nonlinear oil-film force, and nonlinear gear mesh force.
Abstract: This study performs a systematic analysis of the dynamic behavior of a gear-bearing system with nonlinear suspension, nonlinear oil-film force, and nonlinear gear mesh force. The dynamic orbits of the system are observed using bifurcation diagrams plotted with both the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincare maps, Lyapunov exponents, and fractal dimensions of the gear-bearing system. The numerical results reveal that the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors. The results presented in this study provide an understanding of the operating conditions under which undesirable dynamic motion takes place in a gear-bearing system and therefore serves as a useful source of reference for engineers in designing and controlling such systems.
55 citations
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TL;DR: In this technical note, the Hopf bifurcation in Chen's system is studied and some corresponding dynamics are discussed briefly.
Abstract: In this technical note, the Hopf bifurcation in Chen's system is studied. Some corresponding dynamics are also discussed briefly.
55 citations
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TL;DR: The bifurcation analysis of a predator–prey system of Holling and Leslie type with constant-yield prey harvesting is carried out and it is shown that the model has a Bogdanov–Takens singularity of codimension at least 4 for some parameter values.
Abstract: The bifurcation analysis of a predator–prey system of Holling and Leslie type with constant-yield prey harvesting is carried out in this paper It is shown that the model has a Bogdanov–Takens singularity (cusp case) of codimension at least 4 for some parameter values Various kinds of bifurcations, such as saddle-node bifurcation, Hopf bifurcation, repelling and attracting Bogdanov–Takens bifurcations of codimensions 2 and 3, are also shown in the model as parameters vary Hence, there are different parameter values for which the model has a limit cycle, a homoclinic loop, two limit cycles, or a limit cycle coexisting with a homoclinic loop These results present far richer dynamics compared to the model with no harvesting Numerical simulations, including the repelling and attracting Bogdanov–Takens bifurcation diagrams and corresponding phase portraits, and the existence of two limit cycles or an unstable limit cycle enclosing a stable multiple focus with multiplicity one, are also given to support the theoretical analysis
55 citations
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TL;DR: In this article, a simple multiplier-accelerator model of the business cycle including a cubic nonlinearity is presented, where the corresponding two dimensional iterative map is represented in terms of its bif...
Abstract: This paper deals with a simple multiplier-accelerator model of the business cycle, including a cubic nonlinearity. The corresponding two dimensional iterative map is represented in terms of its bif ...
55 citations