Results 31 to 40 of about 636 (179)

Generalized homoclinic solutions for the Swift–Hohenberg equation

Journal of Mathematical Analysis and Applications, 2012
The authors study the Swift-Hohenberg equation, which depends on one parameter and describes the onset of the Rayleigh-Bénard heat convection. By giving an explicit construction, they prove the existence of a homoclinic solution connecting a periodic orbit for every positive parameter.
Deng, Shengfu, Li, Xiaopei
openaire   +1 more source

T(w)o Patch or Not T(w)o Patch: A Novel Biocontrol Model

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT A number of top‐down biocontrol models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest‐dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest‐dependent
Urvashi Verma, Aniket Banerjee, Rana D. Parshad   +2 more
wiley   +1 more source

Fractional Moment Theory for Anomalous Transport: A Unified Framework for Lévy Flights, Fractals, and Complex Dynamical Systems

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley   +1 more source

Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting

Journal of Applied Mathematics, 2014
Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the ...
Mingzhan Huang, Xinyu Song
doaj   +1 more source

Homoclinic Solutions for a Class of Hamiltonian Systems

Advanced Nonlinear Studies, 2004
Abstract We consider the first order Hamiltonian system q̇ = Hp(p, q), ṗ = −Hq(p, q), (HS) where p, q : ℝ → ℝ N (N ≥ 3), H ∈ C 1 (ℝ N × ℝ
openaire   +2 more sources

Homoclinic Solutions of an Integral Equation: Existence and Stability

Journal of Differential Equations, 1999
The authors study (stationary) evolution equation in the form of the following nonlinear convolution type integral equation \[ (J\ast u)(x)- u(x)-f[u(x)]=0,\tag{1} \] with the condition \(u(\pm \infty)=0.\) It is assumed, that \(J(z)\geq 0\), \(\int J(z) dz =1\) and \(f\) is bistable. They construct homoclinic (even) solutions to the equation (1).
Chmaj, Adam, Ren, Xiaofeng
openaire   +2 more sources

On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop

Tellus: Series A, Dynamic Meteorology and Oceanography, 2018
In this study, we discuss the role of the linear heating term and nonlinear terms associated with a non-linear feedback loop in the energy cycle of the three-dimensional (X–Y–Z) non-dissipative Lorenz model (3D-NLM), where (X, Y, Z) represent the ...
B.-W. Shen
doaj   +1 more source

Homoclinic solutions for second order Hamiltonian systems with general potentials near the origin

Electronic Journal of Qualitative Theory of Differential Equations, 2013
In this paper, we study the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems with general potentials near the origin. Recent results from the literature are generalized and significantly improved.
Qingye Zhang
doaj   +1 more source

Multiple Periodic solutions and Positive Homoclinic Solution for a differential equation

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013
The authors consider the nonautonomous differential equation \[ x''-a(t)x+b(t)x^2+c(t)x^3=0, \] where \(a,b\) and \(c\) are continuous \(T\)-periodic functions and obtain two results for them. The first one gives, under certain additional hypotheses, the existence of at least two nontrivial \(T\)-periodic solutions.
de Araujo, Anderson L. A., Pedroso, Kennedy Martins   +1 more
openaire   +3 more sources

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source