Results 71 to 80 of about 10,534 (236)

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
openaire   +5 more sources

HOMOCLINIC ORBITS OF NONPERIODIC SUPERQUADRATIC HAMILTONIAN SYSTEM [PDF]

Taiwanese Journal of Mathematics, 2009
The authors consider the Hamiltonian system \[ \dot{u} = JH_u(t,u) \] where \[ H(t,u) = {{1}\over{2}}u^*Lu + W(t,u) \] and \(L\) is symmetric constant and \(W(t,u)\) is subject to some technical assumptions connected to super quadratic character. The main result of the paper is that under the assumptions mentioned above the system has at least one ...
Zhang, Jian, Tang, Xianhua, Zhang, Wen
openaire   +3 more sources

New Solutions of Breaking Soliton Equation Using Softmax Method

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This study presents the application of a novel Softmax method to obtain exact analytical solutions of the breaking soliton equation, a nonlinear partial differential equation that models complex wave phenomena. By transforming the governing equation into an ordinary differential equation using a traveling wave transformation and constructing a solution
Nguyen Minh Tuan, Phayung Meesad, Nguyen Hong Son, Kannan Krithivasan   +3 more
wiley   +1 more source

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

, 1996
We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to ...
Aizawa Y, Arnold V I, Azuma T, Bicak J, Biesiada M, Bombelli L, Cerjan C, Charlier C L, Contopoulos G, Contopoulos G, Curzon H E J, D Hobill, Dettmann C P, Eckhardt B, Karas V, Kei-ichi Maeda, Kramar D, Maeda K, Misner C W, Moeckel R, Ong C P, Press W, Rugh S E, Shimada I, Shingo Suzuki, Sota Y, Szydlowski M, Toda M, Varvoglis H, Wiggins S, Yasuhide Sota, Zipoy M   +31 more
core   +1 more source

Pseudoholomorphic curves and multiplicity of homoclinic orbits [PDF]

Duke Mathematical Journal, 1995
The authors consider a Hamiltonian system of the form \[ \dot x = J(x) H'(t;x) \tag{1} \] on a compact, smooth Riemannian manifold \(M\). The function \(H : \mathbb{R} \times TM \to \mathbb{R}\) is smooth, 1-periodic in time and admits a point \(q_0 \in M\) such that \[ H(t; q_0, 0) = 0,\quad H'(t;q_0, 0) = 0, \] \[ H(t; q_0, p) \geq 0,\quad H(t;q,0) <
Cieliebak, Kai, Séré, Eric
openaire   +2 more sources

Stability and Bifurcation Analysis of a Predator–Prey Model With Generalized Allee Effect on the Prey Population

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This research describes a predator–prey system that takes into account the generalized Allee effect, aiming to derive general conclusions applicable to specific Allee effect functions through the use of a generalized function. To make sure the suggested model was accurate from a mathematical perspective, we first investigated the solutions to determine
Gaji Zhuo, Hua Liu, Danyang Li, Qibin Zhang, Yumei Wei, A. M. Nagy   +5 more
wiley   +1 more source

Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System

MATEC Web of Conferences, 2016
In this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems ...
Zhou Sha, Zhang Wei, Yu Tian-jun
doaj   +1 more source

A Note on Homoclinic Orbits for Second Order Hamiltonian Systems [PDF]

, 2014
In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential $V$, we apply the direct method of variations and the Fourier analysis to prove the existence of ...
Li, Bingyu, Li, Fengying, Wu, Donglun, Zhang, Shiqing   +3 more
core  

Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model

, 2018
We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that describes dynamics in a food chain "prey-predator-superpredator".
Bakhanova, Yu. V., Kazakov, A. O., Korotkov, A. G., Levanova, T. A., Osipov, G. V.   +4 more
core   +1 more source

Research on Chaotic Threshold of Giant Magnetostrictive Actuator With Fractional‐Order Time‐Delay Feedback

Shock and Vibration, Volume 2025, Issue 1, 2025.
To reduce the giant magnetostrictive actuator’s (GMA) irregular vibration caused by system parameter changes, we innovatively apply fractional‐order time‐delay feedback to control bifurcation and chaos in the GMA’s nonlinear dynamics. The GMA dynamic equation with feedback control is established using the quadratic domain rotation model, the Jiles ...
Xin Fu, Hongbo Yan, Chaohui Ai, Jianxin Wang, Yan Niu   +4 more
wiley   +1 more source