This paper presents a bipedal model with asymmetric leg motion under two-parameter pulse thrust, represented by an impulsive hybrid system. By exploring the successive and immediate transitions in states, Poincaré map explicit form is designed to reveal dynamic characteristics of walking. The stability periodic orbits during walking regulation, as well bifurcation mechanism locomotion, discussed. simulation results about gait, flip bifurcation, chaotic control are agreement theoretical...

In this paper, we have investigated the restricted 14-vortex problem with a honeycomb configuration similar to football surface pattern. First, give sufficient condition for existence of configurations and obtain instability configurations. Then, establish equation motion tracer particle analyze stability distribution equilibrium points singular points. As can be seen from global phase diagram system, there are only four types orbits: points, homoclinic orbits, heteroclinic periodic orbits.

In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon dynamics BECs. Using aver- aging method, determine location where modulated amplitude waves (periodic or quasi-periodic) exist also study stability instability quasi-periodic). Compared with previous work, studied in have nontrivial phases makes problem become more diffcult, since it involves some singularities.

<title>Abstract</title> In this paper, we obtain sufficient and necessary conditions for self-similar motions of three point vortices in generalized two-dimensional fluid systems by reducing Hamiltonian developing the theory functions. The results are concise clear, occurrence both collapse expansion only depend on strengths vortices. We have provided an explicit exact expression each nontrivial solution. application theoretical Surface-Quasi-Geostrophic system is consistent with previous...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 July 2020Accepted: 10 November 2020Published online: 21 January 2021Keywordspoint-vortex, singularity, stability, Moser's twist theoremAMS Subject Headings37J25, 34D20, 76B47Publication DataISSN (online): 1536-0040Publisher: Society for Industrial and Applied MathematicsCODEN: sjaday

In this paper, we investigate the dynamics of three-vortex systems and give a global phase diagram analysis with different types parameters on plane. By using invariants to construct canonical transformations, Hamiltonian system is reduced desired two-dimensional Hamiltonian. Then, analyze its diagrams by considering all possible situations. each case, stabilities equilibrium points singular are established numerical methods, obtain distribution trajectories in space.

In this paper, we give an explicit nondegeneracy condition for the existence of Kolmogorov-Arnold-Moser (KAM) tori N-point vortex system on plane by using method reduction via generalized Jacobi coordinates and matrix theory. Furthermore, constructing a series canonical transformations to reduce degree freedom Hamiltonian, obtain new simplified Hamiltonian system. Finally, equivalent relationship between relative equilibrium point original

Abstract In this paper, we investigate the finite‐time stability (FTS) and control of nonlinear Hamiltonian systems with time‐varying state delays output subject to input saturation. By introducing a new class Lyapunov–Krasovskii (L‐K) functionals assumption about function, present delay‐dependent FTS criterion. Then, feedback is designed for systems. Finally, validity proposed results demonstrated by numerical example.

Motivated by some physical models with small parameters, in this paper, we proved the existence of periodic solutions (almost solutions) for two classes differential equations attractive–repulsive singularities and time‐dependent coefficients averaging method implicit function theorem. Copyright © 2012 John Wiley &amp; Sons, Ltd.

We apply the averaging method to analyze spatio-temportal structures in nonlinear Schrödinger equations and thereby study dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with scattering length varying periodically space crossing zero.Infinitely many modulated amplitude waves nontrivial phases are shown.

We study the existence of modulated amplitude waves with non-trivial phase a quasi-1D multicomponent Bose–Einstein condensate (BEC) in presence an external periodic potential. Mathematically, such coherent structures are doubly solutions, space and time, coupled system Gross–Pitaevskii equations. For binary BEC, weak interaction regime is tackled by means averaging method regular perturbation theory. The case strong particle covered simple rescaling argument. One components stationary, while...

&lt;p style='text-indent:20px;'&gt;In this paper, we shall give new insights on dynamics of contact Hamiltonian flows, which are gaining importance in several branches physics as they model a dissipative behaviour. We divide the phase space into three parts, corresponding to differential invariant sets &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \Omega_\pm, \Omega_0 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. On id="M2"&gt;\begin{document}$ \Omega_\pm...

In this paper, we investigate the stability of port-Hamiltonian systems with mixed time-varying delays as well input saturation. Three types time delays, including state delay, and output are all assumed to be bounded. By introducing feedback control law utilizing serval Lyapunov–Krasovskii functionals, present three delay-dependent criteria in terms linear matrix inequality. Meanwhile, use Wirtinger’s inequality, constraint conditions, functionals triple quadruple integral form obtain less...