Results 31 to 40 of about 717,589 (231)
Existence of homoclinic orbit for second-order nonlinear difference equation
Electronic Journal of Qualitative Theory of Differential Equations, 2010 By using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation $\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0$ has at least one homoclinic orbit, where $t\in \mathbb{Z},\ u\in ...
Peng Chen, Li Xiao
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Mathematics, 2023 In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave ...
Mengke Yu, Cailiang Chen, Qiuyan Zhang
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Bifurcation Analysis of Nonlinear Oscillations in the Electrical Activity of Pancreatic β‐Cells
PAMM, Volume 25, Issue 4, December 2025.ABSTRACT Cell biological systems are characterized by complex relationships and nonlinear processes. The modeling of these processes improves the understanding, and represents a significant enrichment of the experimental investigation. An example of such a system is the regulation of blood glucose concentration by pancreatic β$\beta$‐cells through the ...
Paula Clasen +2 more
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Quantitative Biology, Volume 13, Issue 3, September 2025.Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Peng Zhang +3 more
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Characterization of K-complexes and slow wave activity in a neural mass model.
PLoS Computational Biology, 2014 NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3.
Arne Weigenand +4 more
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Complexity, 2020 In this paper, mathematical models for the management of biological resources based on a given predator-prey relationship are proposed, and two types of control strategies, unilateral and bilateral control with impulsive state feedback, are studied.
Mingzhan Huang +3 more
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Basins of attraction in a modified ratio-dependent predator-prey model with prey refugee
AIMS Mathematics, 2022 In this paper, we analyze a modified ratio-dependent predator-prey model with a strong Allee effect and linear prey refugee. The model exhibits rich dynamics with the existence of separatrices in the phase plane in-between basins of attraction associated
Khairul Saleh
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Closed geodesics and the first Betti number
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We prove that, on any closed manifold of dimension at least two with non‐zero first Betti number, a C∞$C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Mañé together with the following new theorem of ...
Gonzalo Contreras, Marco Mazzucchelli
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Homoclinic orbits and Lie rotated vector fields
International Journal of Mathematics and Mathematical Sciences, 2000 Based on the definition of Lie rotated vector fields in the plane, this paper gives the property of homoclinic orbit as parameter is changed and the singular points are fixed on Lie rotated vector fields.
Jie Wang, Chen Chen
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Spatial dynamics in the family of sixth-order differential equations from the theory of partial formation [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамикаTopic of the paper. Bounded stationary (i.e. independent in time) spatially one-dimensional solutions of a quasilinear parabolic PDE are studied on the whole real line.
Kulagin, Nikolaj Evgenevich +1 more
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