Results 71 to 80 of about 205,637 (167)
Homoclinic orbits to invariant tori near a homoclinic orbit to center-center-saddle equilibrium [PDF]
, 2003 We consider a perturbation of an integrable Hamiltonian vector field with three degrees of freedom with a center–center–saddle equilibrium having a homoclinic orbit or loop. With the help of a Poincaré map (chosen based on the unperturbed homoclinic loop)
Delshams Valdés, Amadeu +3 more
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Bifurcation Analysis of Nonlinear Oscillations in the Electrical Activity of Pancreatic β‐Cells
Proceedings in Applied Mathematics and Mechanics, Volume 25, Issue 4, December 2025.ABSTRACT Cell biological systems are characterized by complex relationships and nonlinear processes. The modeling of these processes improves the understanding, and represents a significant enrichment of the experimental investigation. An example of such a system is the regulation of blood glucose concentration by pancreatic β$\beta$‐cells through the ...
Paula Clasen +2 more
wiley +1 more source
Global bifurcation of a cubic system perturbed by degree four
上海师范大学学报. 自然科学版, 2014 Using the method of multi-parameter perturbation theory and qualitative analysis, a cubic system perturbed by degree four are investigated in this paper. After systematic analysis, it is found that the studied system can have nine limit cycles with their
Desheng Shang, Zheng Wang
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On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^1$
Electronic Journal of Qualitative Theory of Differential EquationsShilnikov's scenario in $\mathbb{R}^3$ means that the equation $x'=V(x)\in\mathbb{R}^3$ with $V(0)=0$ has a homoclinic solution and the eigenvalues of $DV(0)$ are $u>0$ and $\sigma\pm i\mu$ with ...
Hans-Otto Walther
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Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
, 2020 The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence
Zhiqin Qiao, Yancong Xu
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Exploring the Influence of Oblateness on Asymptotic Orbits in the Hill Three-Body Problem
AppliedMathWe examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear ...
Vassilis S. Kalantonis
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Codimension 2 bifurcation of twisted double homoclinic loops [PDF]
, 2009 A local active coordinates approach is employed to obtain bifurcation equations of twisted double homoclinic loops. Under the condition of one twisted orbit, we obtain the existence and uniqueness and of the 1–1 double homoclinic loop, 2–1 double ...
Lu, Qiuying
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Homoclinic bifurcations in a planar dynamical system
, 2022 S.1183-1191The homoclinic bifurcation properties of a planar dynamical system are analyzed and the corresponding bifurcation diagram is presented. The occurrence of two Bogdanov-Takens bifurcation points provides two local existing curves of homoclinic ...
Kuepper, T., Giannakopoulos, F., Zou, Y.
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Existence of homoclinic orbits for a class of nonlinear functional difference equations
Electronic Journal of Differential Equations, 2016 By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz ...
Xia Liu, Tao Zhou, Haiping Shi
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Robust homoclinic orbits in planar systems with Preisach hysteresis operator [PDF]
, 2016 We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time.
Pimenov, Alexander, Rachinskii, Dmitrii
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