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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng
Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng
Department of Mathematics: Faculty Publications
Here we prove that the dynamics on any two center-manifolds of a fixed point of any Ck,1 dynamical system of finite dimension with k ≥ 1 are Ck-conjugate to each other. For pedagogical purpose, we also extend Perron’s method for differential equations to diffeomorphisms to construct the theory of invariant manifolds and invariant foliations at fixed points of dynamical systems of finite dimensions.
On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov
On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov
Turkish Journal of Mathematics
We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation $\Delta y(n)=-g(n)y(n-k)$. We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as $n\to\infty$. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotic formulae. The obtained results are applied to the oscillation and stability problems for the solutions of the considered equation.
Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang
Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang
CODEE Journal
One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is …
A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn
A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn
Mathematics and Statistics Faculty Publications
When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ''Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theory using a finite number of excited spatial modes. We establish such a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces developed by da Prate and Grisvard, establish maximal regularity for a family of evolution …
Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng
Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng
Department of Mathematics: Faculty Publications
A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil'nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem.