Xianbo Sun

SOME BIFURCATION RESULTS IN NEAR-HAMILTONIAN SYSTEMS WITH FINITE-ORDER SMOOTHNESS

Ci Kong, Maoan Han, Yun Tian, Xianbo Sun

This paper presents a systematic survey of bifurcation theory for near-Hamiltonian systems with finite-order smoothness. Unlike the classical $C^{\infty}$ or $C^{\omega}$ framework, we collect some known results on limit cycle bifurcations for planar systems with finite-order smoothness, including Poincaré bifurcation, Hopf bifurcation, …

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Melnikov analysis in the complex cubic-quintic Ginzburg-Landau equation with higher-order dispersion

Xianbo Sun, Pei Yu, Mingji Zhang

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Mechanistic insights into zero-valent-cobalt-driven self-sustaining Fenton process via selective oxygen reduction to generate hydrogen peroxide

Yu Shrike Zhang, Mingtao Liu, Yongdi Liu, Yanyu Song et autres

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Heteroclinic bifurcation near a loop tangent to an invariant line

Xianbo Sun, Guilin Ji, Qun Bin

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Dynamics of a quartic Korteweg–de Vries equation with multiple dissipations via an Abelian integral approach

Xianbo Sun, Mingji Zhang

We analyze both solitary and periodic wave solutions of a quartic Korteweg-de Vries (KdV) equation that incorporates multiple dissipative effects. The investigation primarily focuses on the dynamical behavior within a two-dimensional invariant manifold. To establish the existence of solitary waves, we employ …

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Homoclinic Bifurcation from Perturbing a Cubic Integrable and Non-Hamiltonian System

Wen Hua Qian, Wentao Huang, Xianbo Sun

In this paper, we examine homoclinic bifurcation in a planar cubic integrable system, incorporating cubic polynomial perturbations, by employing first-order and second-order Melnikov functions. We derive the simplest expressions for these two Melnikov functions and their asymptotic expansions in proximity to the …

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Small-amplitude periodic solutions in the polynomial jerk equation of arbitrary degree

Jaume Llibre, Xianbo Sun

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Homoclinic bifurcation near a loop tangent to an invariant straight line

Xianbo Sun, Yun Tian, Maoan Han

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Existence and stability of traveling waves in a Keller-Segel system with nonlinear stimulation

Xianbo Sun, Wentao Huang, Yuchen Wang

Abstract In this article, we reformulate the Keller-Segel model by incorporating a nonlinear cellular stimulation term. We then investigate its dynamical behavior by reducing the Keller-Segel model to a dynamical system on a two-dimensional invariant flow. Our analysis confirms the existence of …

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A bi-layer optimization method of the grid-connected microgrid based on the multi-strategy of the beluga whale algorithm

Xianjing Zhong, Xianbo Sun, Yuhan Wu

Endeavoring to enhance the penetration rate of renewable energy sources, concurrently ensuring economic and operational stability, this study proposes a novel bi-layer optimization method of the wind–solar-storage AC/DC microgrid (MG). First, by incorporating a superordinate electric and seasonal hydrogen hybrid energy storage …

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MONOTONICITY OF THE RATIOS OF TWO ABELIAN INTEGRALS FOR HAMILTONIAN SYSTEMS WITH PARAMETERS

Qiaoyun Wang, Na Wang, Xianbo Sun

We study the monotonicity of the ratios of two Abelian integrals $ \oint_{\gamma_{i}(h)}ydx $ $ \backslash $ $ \oint_{\gamma_{i}(h)}xydx $ over three period annuli $ \{\gamma_i(h)\} $, for $ i=1, 2, 3 $, defined by a seventh-degree hyperelliptic Hamiltonian $ H(x, y)=y^2+\Psi(x) …

Multi-obje Optimization Strategy for Distributed Energy Resources in Distribution Networks Based on a Two-Stage Model

Zhichao Wang, Xianbo Sun, Yiluo Ke

With the rapid development of new energy, a large number of distributed generation (DG) are connected to the distribution network. As the number of DGs connected to the grid increases, it will exacerbate voltage fluctuations and instability in the power grid, which …

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