Invariant manifold of hyperbolic-elliptic type for nonlinear wave equation by Xiaoping Yuan

Get full text

Integral invariant manifold method applied to a mathematical model of osteosarcoma by Ophir Nave

Subjects: Get full text

Invariant manifolds and alternative approaches to reductive perturbation theory: dissipative systems by Hedley C. Morris, Derek Sheil, Roger Dodd

Subjects: Get full text

Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under (μ,ν)-Dichotomies by Lijun Pan

“…We show that the stable invariant manifolds are dependent on parameter λ. Namely, the stable invariant manifolds are Lipschitz in the parameter λ. …”
Get full text

On Complex Dynamics of Differentiated Products: Cournot Duopoly Model under Average Profit Maximization by S.S. Askar

“…Under some restrictions, the map’s coordinate axes form an invariant manifold, and hence their dynamics are studied based on a one-dimensional discrete dynamic map. …”
Get full text

Characterization of the dynamic behavior of nonlinear biosystems in the presence of model uncertainty using singular invariance PDEs: Application to immobilized enzyme and... by Nikolaos Kazantzis, Vasiliki Kazantzi

“…Within the class of analytic solutions, this set of conditions guarantees the existence and uniqueness of a locally analyticsolution which represents the system's slow invariant manifold exponentially attracting all dynamic trajectories in the absence of model uncertainty. …”
Get full text

Blowout bifurcation of chaotic saddles by Tomasz Kapitaniak, Ying-Cheng Lai, Celso Grebogi

“…We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.…”
Get full text

Chaos and shadowing around a homoclinic tube by Yanguang (Charles) Li

“…F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. …”
Get full text

Traveling Wave Solution in a Diffusive Predator-Prey System with Holling Type-IV Functional Response by Deniu Yang, Lihan Liu, Hongyong Wang

“…The methods used to prove the result are the shooting argument and the invariant manifold theory.…”
Get full text

Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems by Chein-Shan Liu

“…To solve an unconstrained nonlinear minimization problem, we propose an optimal algorithm (OA) as well as a globally optimal algorithm (GOA), by deflecting the gradient direction to the best descent direction at each iteration step, and with an optimal parameter being derived explicitly. An invariant manifold defined for the model problem in terms of a locally quadratic function is used to derive a purely iterative algorithm and the convergence is proven. …”
Get full text

Cournot–Bertrand Duopoly Model: Dynamic Analysis Based on a Computed Cost by S. S. Askar, Ahmed M. Alshamrani

“…One of those fixed points is Nash equilibrium, and the discussion shows that it can be unstable through flip and Neimark–Sacker bifurcation. The invariant manifold for the game’s map is analyzed. Furthermore, the case when both competing firms are independent is investigated. …”
Get full text

Detecting phase transitions in collective behavior using manifold's curvature by Kelum Gajamannage, Erik M. Bollt

“…If a given behavior of a multi-agent system restricts the phase variable to an invariant manifold, then we define a phase transition as a change of physical characteristics such as speed, coordination, and structure. …”
Get full text

Nonlinear Normal Modes in a Two-Stage Isolator Using a Modified Finite-Element Galerkin Method by Cheng Li, Hongguang Li

“…The presented approach applies a combination of finite-element discretization and Fourier series expansion for the approximate invariant manifolds. A Galerkin projection of the governing equations for the approximate invariant manifolds yields a set of nonlinear algebraic equations in expansion coefficients, which can be solved numerically with a general choice of zero as initial guess for the cases in this work. …”
Get full text

The Neimark–Sacker Bifurcation and Global Stability of Perturbation of Sigmoid Beverton–Holt Difference Equation by M. R. S. Kulenović, Connor O’Loughlin, E. Pilav

“…Furthermore, we give the asymptotic approximation of the invariant manifolds, stable, unstable, and center manifolds of the equilibrium solutions. …”
Get full text