This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These model...This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These models offer valuable insights into nonlinear wave propagation,with applications in fluid dynamics and materials science,including systems such as liquid crystals and ferrofluids.It is shown that the conservative Sawada-Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles,as well as two-and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation(ODE)system.For the dissipative generalized Sawada-Kotera equation,chaotic wave behavior is observed.The transition to chaos in the corresponding ODE systemfollows a universal bifurcation scenario consistent with the framework established by FShM(Feigenbaum-Sharkovsky-Magnitskii)theory.Notably,this study demonstrates for the first time that the conservative Sawada-Kotera equation can exhibit complex quasi-periodic wave solutions,while its dissipative counterpart admits an infinite number of stable periodic and chaotic waveforms.展开更多
基于经验模式分解(empirical mode decomposition,简称EMD)分解出的基本模式分量往往会因为原始数据中的一些异常数据和高频噪声而丧失明确的物理意义。因此,提出了一种基于系统重构吸引子奇异值分解(singular value decomposition,简称...基于经验模式分解(empirical mode decomposition,简称EMD)分解出的基本模式分量往往会因为原始数据中的一些异常数据和高频噪声而丧失明确的物理意义。因此,提出了一种基于系统重构吸引子奇异值分解(singular value decomposition,简称SVD)降噪的EMD分解方法。在改进方法中,原始信号经SVD降噪后分解出了原信号中的有用成分和冗余成分,对有用成分进行EMD分解可以减少原信号中冗余成分对EMD分解能力的干扰,提高EMD分解能力,使得分解出的基本模式分量更加具有实际意义,更加有利于特征的提取。展开更多
Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky...Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.展开更多
In this paper,we consider the families of nearby singular diffeomorphism and the measure of a set in the parameter space,such that for each point of the set the corresponding diffeomorphism possesses strange attractor...In this paper,we consider the families of nearby singular diffeomorphism and the measure of a set in the parameter space,such that for each point of the set the corresponding diffeomorphism possesses strange attractor.For some families of one-dimensional mapping satisfying certain transversality condition,we prove that there is a positive measure set in the parameter space, such that the system in the corresponding families of nearly singular diffeomorphism has strange attractor.Furthermore,we study the dynamics of this type of strange attractor.展开更多
In this paper,we study the Sil’nikov heteroclinic bifurcations,which display strange attractors,for the symmetric versal unfoldings of the singularity at the origin with a nilpotent linear part and 3-jet,using the no...In this paper,we study the Sil’nikov heteroclinic bifurcations,which display strange attractors,for the symmetric versal unfoldings of the singularity at the origin with a nilpotent linear part and 3-jet,using the normal form,the blow-up and the generalized Mel’nikov methods of heteroclinic orbits to two hyperbolic or nonhyperbolic equilibria in a high-dimensional space.展开更多
文摘This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These models offer valuable insights into nonlinear wave propagation,with applications in fluid dynamics and materials science,including systems such as liquid crystals and ferrofluids.It is shown that the conservative Sawada-Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles,as well as two-and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation(ODE)system.For the dissipative generalized Sawada-Kotera equation,chaotic wave behavior is observed.The transition to chaos in the corresponding ODE systemfollows a universal bifurcation scenario consistent with the framework established by FShM(Feigenbaum-Sharkovsky-Magnitskii)theory.Notably,this study demonstrates for the first time that the conservative Sawada-Kotera equation can exhibit complex quasi-periodic wave solutions,while its dissipative counterpart admits an infinite number of stable periodic and chaotic waveforms.
文摘基于经验模式分解(empirical mode decomposition,简称EMD)分解出的基本模式分量往往会因为原始数据中的一些异常数据和高频噪声而丧失明确的物理意义。因此,提出了一种基于系统重构吸引子奇异值分解(singular value decomposition,简称SVD)降噪的EMD分解方法。在改进方法中,原始信号经SVD降噪后分解出了原信号中的有用成分和冗余成分,对有用成分进行EMD分解可以减少原信号中冗余成分对EMD分解能力的干扰,提高EMD分解能力,使得分解出的基本模式分量更加具有实际意义,更加有利于特征的提取。
文摘Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.
基金Project Supported by Fund of National Science of China
文摘In this paper,we consider the families of nearby singular diffeomorphism and the measure of a set in the parameter space,such that for each point of the set the corresponding diffeomorphism possesses strange attractor.For some families of one-dimensional mapping satisfying certain transversality condition,we prove that there is a positive measure set in the parameter space, such that the system in the corresponding families of nearly singular diffeomorphism has strange attractor.Furthermore,we study the dynamics of this type of strange attractor.
文摘In this paper,we study the Sil’nikov heteroclinic bifurcations,which display strange attractors,for the symmetric versal unfoldings of the singularity at the origin with a nilpotent linear part and 3-jet,using the normal form,the blow-up and the generalized Mel’nikov methods of heteroclinic orbits to two hyperbolic or nonhyperbolic equilibria in a high-dimensional space.
