Results 61 to 70 of about 8,022 (205)
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.This study examines the second‐order Kuramoto model within a specific small invariant subspace. We explore how the damping parameter influences the emergence of synchronized states and the weak chimera state in this model. In addition, we numerically investigate various behaviors in the phase space resulting from changes in the damping parameter and ...
Mary G. Thoubaan +4 more
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Measure-Expansive Homoclinic Classes for C1 Generic Flows
Mathematics, 2020 In this paper, we prove that for a generically C1 vector field X of a compact smooth manifold M, if a homoclinic class H(γ,X) which contains a hyperbolic closed orbit γ is measure expansive for X then H(γ,X) is hyperbolic.
Manseob Lee
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Modeling of Chaotic Processes by Means of Antisymmetric Neural ODEs
Journal of Optimization, Differential Equations and Their Applications, 2022 The main goal of this work is to construct an algorithm for modeling chaotic processes using special neural ODEs with antisymmetric matrices (antisymmetric neural ODEs) and power activation functions (PAFs).
Vasiliy Ye. Belozyorov +1 more
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Homoclinic Orbits and Lagrangian Embeddings [PDF]
International Mathematics Research Notices, 2010 This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Sere and to Coti-Zelati, Ekeland and Sere, which were obtained by variational methods.
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This study presents the dynamic analysis of stochastic fractional unstable nonlinear Schrödinger equation (SFuNLSE), focusing on the analysis of bifurcation, chaotic nature, return map, recurrence plots, strange attractor, basin attractor, power spectrum, chaotic nature and also finds the exact optical soliton solution with multiplicative noise ...
Md. Mamunur Roshid +3 more
wiley +1 more source
Perturbed Li–Yorke homoclinic chaos
Electronic Journal of Qualitative Theory of Differential Equations, 2018 It is rigorously proved that a Li–Yorke chaotic perturbation of a system with a homoclinic orbit creates chaos along each periodic trajectory. The structure of the chaos is investigated, and the existence of infinitely many almost periodic orbits out of ...
Marat Akhmet +3 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.This study investigates the complex dynamics of a predator–prey system governed by the classical Lotka–Volterra model incorporating a Holling‐type III. To capture environmental variability, the prey’s carrying capacity is modeled as a periodic function, introducing a time‐dependent forcing into the system.
Ali Sarrah +4 more
wiley +1 more source
Homoclinic Orbits for First Order Hamiltonian Systems
Journal of Mathematical Analysis and Applications, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Y.H., Li, S.J.
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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
Degenerate Periodic Orbits and Homoclinic Torus Bifurcation
Physical Review Letters, 2005 A one-parameter family of periodic orbits with frequency omega and energy E of an autonomous Hamiltonian system is degenerate when E'(omega) = 0. In this paper, new features of the nonlinear bifurcation near this degeneracy are identified. A new normal form is found where the coefficient of the nonlinear term is determined by the curvature of the ...
Bridges, T J, Donaldson, N M
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