All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 6 Next

Displaying 101 – 120 of 478

Showing per page

Consensus of a two-agent system with nonlinear dynamics and time-varying delay

Ye Cheng, Bao Shi, Liangliang Ding (2021)

Applications of Mathematics

To explore the impacts of time delay on nonlinear dynamics of consensus models, we incorporate time-varying delay into a two-agent system to study its long-time behaviors. By the classical 3/2 stability theory, we establish a sufficient condition for the system to experience unconditional consensus. Numerical examples show the effectiveness of the proposed protocols and present possible Hopf bifurcations when the time delay changes.

Convergence of the Lagrange-Newton method for optimal control problems

Kazimierz Malanowski (2004)

International Journal of Applied Mathematics and Computer Science

Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case,...

Decaying positive solutions of some quasilinear differential equations

Tadie (1998)

Commentationes Mathematicae Universitatis Carolinae

The existence of decaying positive solutions in ℝ + of the equations ( E λ ) and ( E λ 1 ) displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. t 1 - p F ( r , t U , t | U ' | ) ↘ 0 as t ↗ ∞ ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.

Decoupling normalizing transformations and local stabilization of nonlinear systems

S. Nikitin (1996)

Mathematica Bohemica

The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.

Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system

Hongtao Liang, Yanxia Tang, Li Li, Zhouchao Wei, Zhen Wang (2013)

Kybernetika

In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.

Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions

Szabolcs Rozgonyi, Katalin M. Hangos, Gábor Szederkényi (2010)

Kybernetika

In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions V n in a rational functional form approximating a maximal Lyapunov function V M that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions V n for a class of hybrid (piecewise...

Currently displaying 101 – 120 of 478