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Degenerate Fold–Hopf Bifurcations in a Rössler-Type System [PDF]
International Journal of Bifurcation and Chaos, 2017 We study the Hopf and the fold–Hopf bifurcations of the Rössler-type differential system [Formula: see text] with [Formula: see text]. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold–Hopf bifurcation, which here is studied using the averaging theory.
Tigan, Gheorghe +2 more
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Instability of small-amplitude periodic waves from fold-Hopf bifurcation [PDF]
Journal of Mathematical Physics, 2022 We study the existence and stability of small-amplitude periodic waves emerging from fold-Hopf equilibria in a system of one reaction–diffusion equation coupled with one ordinary differential equation. This coupled system includes the FitzHugh–Nagumo system, caricature calcium models, and other models in real-world applications.
Shuang Chen, Jinqiao Duan
openaire +3 more sources
Bursting Oscillations in General Coupled Systems: A Review
Mathematics, 2023 In this paper, the bursting oscillation phenomenon in coupled systems with two time scales is introduced. Firstly, several types of bifurcation are briefly introduced: fold bifurcation, Hopf bifurcation, fold limit cycle bifurcation, homoclinic ...
Danjin Zhang, Youhua Qian
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Fast-Slow Coupling Dynamics Behavior of the van der Pol-Rayleigh System
Mathematics, 2021 In this paper, the dynamic behavior of the van der Pol-Rayleigh system is studied by using the fast–slow analysis method and the transformation phase portrait method.
Danjin Zhang, Youhua Qian
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Modelling and Simulation in Engineering, 2023 Acetyl chloride hydrolysis is a highly sensitive exothermic reaction that has presented several industrial safety issues. In the present study, a multiparameter mathematical model, previously developed and applied to simulate the oscillatory thermal ...
Juan Carlos Ojeda Toro +2 more
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Influence of arginine vasopressin on the ultradian dynamics of Hypothalamic-Pituitary-Adrenal axis
Frontiers in Endocrinology, 2022 Numerous studies on humans and animals have indicated that the corticotrophin-releasing hormone (CRH) and arginine vasopressin (AVP) stimulate both individually and synergistically secretion of adrenocorticotropic hormone (ACTH) by corticotropic cells in
Aleksandra S. Stojiljković +5 more
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Dynamic effect of electromagnetic induction on epileptic waveform
BMC Neuroscience, 2022 Background Electromagnetic induction has recently been considered as an important factor affecting the activity of neurons. However, as an important form of intervention in epilepsy treatment, few people have linked the two, especially the related ...
Yuqin Sun +3 more
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The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability [PDF]
, 2019 We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$.
Ashwin, P. +4 more
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Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow [PDF]
, 2010 The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail.
B. ECKHARDT +6 more
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Bifurcations associated with sub-synchronous resonance [PDF]
, 1998 This paper describes a set of results of detecting nonlinear phenomena appearing in a turbine generator power system with series-capacitor compensation. The analysis was based on the Floquet theory as well as the Hopf bifurcation theorem. After the first
Mitani, Y +4 more
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