Results 51 to 60 of about 1,641 (211)
Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2194-2223, 30 January 2025.The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores ...
Anuj Kumar Umrao +2 more
wiley +1 more source
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems
Electronic Journal of Differential Equations, 1997 Homoclinic orbits play an important role in the study of qualitative behavior of dynamical systems. Such kinds of orbits have been studied since the time of Poincare.
Chao-Nien Chen, Shyuh-Yaur Tzeng
doaj
Homoclinic orbits for a nonperiodic Hamiltonian system
Journal of Differential Equations, 2007 Consider the first order Hamiltonian system \(\overset{.}{z}={\mathcal J}H_{z}(t,z) \) where \(z=(p,q)\in {\mathbb R}^{2N},{\mathcal J} =\left( \begin{matrix} 0 & -I \\ I & 0 \end{matrix} \right) \) and \(H\in C^{1}({\mathbb R}\times {\mathbb R}^{2N},{\mathbb R}) \) has the form \( H\left( t,z\right)=\frac{1}{2}L\left( t\right) z\cdot z+R\left( t,z ...
Ding, Yanheng, Jeanjean, Louis
openaire +4 more sources
IET Generation, Transmission &Distribution, Volume 19, Issue 1, January/December 2025.1. The reactive current injection system has infinite saddle points, and for every saddle point, there are two special lines (the blue lines in Figure 2). When the initial states are situated on the special lines, the final states of the reactive current injection will converge to the saddle points. 2.
Shuaishuai Lv +7 more
wiley +1 more source
Global orbit of a complicated nonlinear system with the global dynamic frequency method
Journal of Low Frequency Noise, Vibration and Active Control, 2021 Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the ...
Zhixia Wang +3 more
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Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.The first‐ and second‐order wave equations of Benjamin–Ono control the propagation of nonlinear Rossby waves in a rotating fluid and define a broad class of internal waves in a stratified fluid of enormous depth. New solitary wave solutions and the modulation instability of the solutions for the first‐ and second‐order Benjamin–Ono partial differential
Wilson Osafo Apeanti +3 more
wiley +1 more source
Existence and concentration of homoclinic orbits for first order Hamiltonian systems
Communications in Analysis and MechanicsThis paper is concerned with the following first-order Hamiltonian system $ \begin{equation} \nonumber \dot{z} = \mathscr{J}H_{z}(t, z), \end{equation} $ where the Hamiltonian function $ H(t, z) = \frac{1}{2}Lz\cdot z+A(\epsilon t)G(|z|) $ and ...
Tianfang Wang, Wen Zhang
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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 +3 more
wiley +1 more source
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 +5 more
wiley +1 more source
Infinitely many homoclinic solutions for a class of nonlinear difference equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee a class of nonlinear difference equation has infinitely many homoclinic orbits. Our conditions on the nonlinear term are rather relaxed and we generalize some
Peng Chen, Zhengmei Wang
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