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Bifurcation Theory: A Review [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2023 Bifurcation theory is a field of mathematics that studies the qualitative changes in the behavior of a dynamical system as a parameter in the system is varied.In this ...
Salma Farris, manal Hamdi
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Homoclinic saddle-node bifurcations in singularly perturbed systems [PDF]
Journal of Dynamics and Differential Equations, 1997 In this paper we study the creation of homoclinic orbits by saddle-node bifurcations. Inspired on similar phenomena appearing in the analysis of so-called “localized structures” in modulation or amplitude equations, we consider a family of nearly integrable, singularly perturbed three dimensional vector fields with two bifurcation parameters a and b ...
Doelman, A., Hek, G.
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Computational Analysis and Bifurcation of Regular and Chaotic Ca2+ Oscillations
Mathematics, 2021 This study investigated the stability and bifurcation of a nonlinear system model developed by Marhl et al. based on the total Ca2+ concentration among three different Ca2+ stores.
Xinxin Qie, Quanbao Ji
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Dynamics of a Filippov epidemic model with limited hospital beds
Mathematical Biosciences and Engineering, 2018 A Filippov epidemic model is proposed to explore the impact of capacity and limited resources of public health system on the control of epidemic diseases.
Aili Wang, Yanni Xiao, Huaiping Zhu
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On the CCN (de)activation nonlinearities [PDF]
Nonlinear Processes in Geophysics, 2017 We take into consideration the evolution of particle size in a monodisperse aerosol population during activation and deactivation of cloud condensation nuclei (CCN). Our analysis reveals that the system undergoes a saddle-node bifurcation and a cusp
S. Arabas, S. Arabas, S.-I. Shima
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Stokes flows in a two-dimensional bifurcation [PDF]
, 2023 The flow network model is an established approach to approximate pressure-flow relationships in a bifurcating network, and has been widely used in many contexts. Existing models typically assume unidirectional flow and exploit Poiseuille's law, and thus neglect the impact of bifurcation geometry and finite-sized objects on the flow.
arxiv +1 more source
Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in R4
Discrete Dynamics in Nature and Society, 2015 We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field in R4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of ...
Tiansi Zhang, Dianli Zhao
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Моделирование и анализ информационных систем, 2015 We consider a finite-dimensional model of phase oscillators with inertia in the case of star configuration of coupling. The system of equations is reduced to a nonlinearly coupled system of pendulum equations.
V. N. Belykh +2 more
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Limits to ecological forecasting: Estimating uncertainty for critical transitions with deep learning
Methods in Ecology and Evolution, 2023 In the current age of a rapidly changing environment, it is becoming increasingly important to study critical transitions and how to best anticipate them. Critical transitions pose extremely challenging forecasting problems, which necessitate informative
Marcus Lapeyrolerie, Carl Boettiger
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On first subharmonic bifurcations in a branch of Stokes waves [PDF]
arXiv, 2023 Steady surface waves in a two-dimensional channel are considered. We study bifurcations, which occur on a branch of Stokes water waves starting from a uniform stream solution. Two types of bifurcations are considered: bifurcations in the class of Stokes waves (Stokes bifurcation) and bifurcations in a class of periodic waves with the period M times the
arxiv