Results 61 to 70 of about 1,285,867 (186)
Nine Limit Cycles in a 5-Degree Polynomials Liénard System
Complexity, 2020 In this article, we study the limit cycles in a generalized 5-degree Liénard system. The undamped system has a polycycle composed of a homoclinic loop and a heteroclinic loop.
Junning Cai, Minzhi Wei, Hongying Zhu
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The general Li\'enard polynomial system [PDF]
, 2012 In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles ...
Gaiko, Valery A.
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On the number of limit cycles in asymmetric neural networks
, 2019 The comprehension of the mechanisms at the basis of the functioning of complexly interconnected networks represents one of the main goals of neuroscience.
Folli, Viola +5 more
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Limit cycles bifurcations of Liénard system with a hyperelliptic Hamiltonian of degree five
Electronic Journal of Qualitative Theory of Differential EquationsWe deal with limit cycles bifurcating from the period annulus of Liénard system with a hyperelliptic Hamiltonian of degree five under quartic perturbation, where Liénard system has a normal form $\dot{x}=y$, $\dot{y}=x(x-1)(x^{2}+ax+b)$, $a^{2 ...
Yi Shao, Chunxiang A
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Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. The presence or absence of limit cycles of polynomial systems constitutes the second part of Hilbert’s well-known 16th problem, which has not yet been completely solved.
V.V. Machulis
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Center conditions and limit cycles for BiLienard systems
Electronic Journal of Differential Equations, 2017 In this article we study the center problem for polynomial BiLienard systems of degree n. Computing the focal values and using Grobner bases we find the center conditions for such systems for n=6.
Jaume Gine
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Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers
Extracta Mathematicae, 2023 We consider a homogeneous degenerate center of order 2m + 1 and perturb it by a homogeneous polynomial of order 2m. We study the Lyapunov constants around the origin to estimate the number of limit cycles.
M. MolaeiDerakhtenjani +2 more
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Bifurcation of limit cycles from quartic isochronous systems
Electronic Journal of Differential Equations, 2014 This article concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quartic homogeneous perturbations, at most two limit cycles bifurcate from the period ...
Linping Peng, Zhaosheng Feng
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Limit Cycles Bifurcated from Some Z4-Equivariant Quintic Near-Hamiltonian Systems
Abstract and Applied Analysis, 2014 We study the number and distribution of limit cycles of some planar Z4-equivariant quintic near-Hamiltonian systems. By the theories of Hopf and heteroclinic bifurcation, it is proved that the perturbed system can have 24 limit cycles with some new ...
Simin Qu +3 more
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Bifurcation of limit cycles for cubic reversible systems
Electronic Journal of Differential Equations, 2014 This article is concerned with the bifurcation of limit cycles of a class of cubic reversible system having a center at the origin. We prove that this system has at least four limit cycles produced by the period annulus around the center under cubic ...
Yi Shao, Kuilin Wu
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