共查询到20条相似文献,搜索用时 15 毫秒
1.
Timoteo Carletti 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(4):559-571
We study the orbit behaviour of a germ of an analytic vector field of
We prove that if its linear part is semisimple, non–resonant and verifies a Bruno–like condition, then the origin is effectively stable: stable for finite but exponentially long times.Received: July 5, 2004; revised: December 9, 2004 相似文献
2.
The problem of delay-dependent asymptotic stability criteria for neural networks (NNs) with time-varying delays is investigated. An improved linear matrix inequality based on delay-dependent stability test is introduced to ensure a large upper bound for time-delay. A new class of Lyapunov function is constructed to derive a novel delay-dependent stability criteria. Finally, numerical examples are given to indicate significant improvement over some existing results. 相似文献
3.
In this note we prove that a Lyapunov stable map having the average-shadowing property from a compact metric space onto itself is topologically ergodic, but it is not topologically weakly mixing. 相似文献
4.
Xiang Zhang 《Journal of Differential Equations》2008,244(5):1080-1092
This paper provides the normal forms of analytic integrable differential systems and diffeomorphisms via analytic normalizations. Furthermore, we consider the existence of embedding flows of an analytic integrable diffeomorphism. 相似文献
5.
6.
In this paper we present an alternative algorithm for computing Poincaré-Lyapunov constants of simple monodromic singularities of planar analytic vector fields based on the concept of inverse integrating factor. Simple monodromic singular points are those for which after performing the first (generalized) polar blow-up, there appear no singular points. In other words, the associated Poincaré return map is analytic. An improvement of the method determines a priori the minimum number of Poincaré-Lyapunov constants which must cancel to ensure that the monodromic singularity is in fact a center when the explicit Laurent series of an inverse integrating factor is known in (generalized) polar coordinates. Several examples show the usefulness of the method. 相似文献
7.
We introduce a class of differential equations on variable time scales with a transition condition between two consecutive parts of the scale. Conditions for existence and uniqueness of solutions are obtained. Periodicity, boundedness and stability of solutions are considered. The method of investigation is by means of two successive reductions: B-equivalence of the system [E. Akalín, M.U. Akhmet, The principles of B-smooth discontinuous flows, Computers and Mathematics with Applications 49 (2005) 981–995; M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163–178; M.U. Akhmet, N.A. Perestyuk, The comparison method for differential equations with impulse action, Differential Equations 26 (9) (1990) 1079–1086] on a variable time scale to a system on a time scale, a reduction to an impulsive differential equation [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163–178; M.U. Akhmet, M. Turan, The differential equations on time scales through impulsive differential equations, Nonlinear Analysis 65 (2006) 2043–2060]. Appropriate examples are constructed to illustrate the theory. 相似文献
8.
A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations—the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution—are obtained. Appropriate examples are constructed. 相似文献
9.
José F. Alves Carla L. Dias Stefano Luzzatto 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2013
We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs–Markov–Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of an invariant probability measure which is absolutely continuous measure (with respect to Lebesgue) and for which all Lyapunov exponents are positive. 相似文献
10.
In this paper we provide a characterization of local integrability for analytic or formal differential systems in Rn or Cn via the integrability varieties. Our result generalizes the classical one of Poincaré and Lyapunov on local integrability of planar analytic differential systems to any finitely dimensional analytic differential systems. As an application of our theory we study the integrability of a family of four-dimensional quadratic Hamiltonian systems. 相似文献
11.
This paper discusses the periodic boundary value problem for first-order nonlinear impulsive integro-differential equations. We prove some new comparison principles, and then establish new existence results for extremal solutions by using these principles and the monotone iterative technique. These results improve and extend all known relevant conclusions from the literature. Some examples are also given to illustrate the advantage of our results. 相似文献
12.
In this work we study the narrow relation between reversibility and the center problem and also between reversibility and the integrability problem. It is well known that an analytic system having either a non-degenerate or nilpotent center at the origin is analytically reversible or orbitally analytically reversible, respectively. In this paper we prove the existence of a smooth map that transforms an analytic system having a degenerate center at the origin with either an analytic first integral or a C∞ inverse integrating factor into a reversible linear system (after rescaling the time). Moreover, if the degenerate center has an analytic or a C∞ reversing symmetry, then the transformed system by the map also has a reversing symmetry. From the knowledge of a first integral near the center we give a procedure to detect reversing symmetries. 相似文献
13.
José F. Alves Maria Carvalho Jorge Milhazes Freitas 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
We consider the family of Hénon maps in the plane and show that the SRB measures vary continuously in the weak∗ topology within the set of Benedicks–Carleson parameters. 相似文献
14.
Javier Ribón 《Journal of Differential Equations》2012,253(12):3211-3231
In [Xiang Zhang, The embedding flows of C∞ hyperbolic diffeomorphisms, J. Differential Equations 250 (5) (2011) 2283-2298] Zhang proved that any local smooth hyperbolic diffeomorphism whose eigenvalues are weakly nonresonant is embedded in the flow of a smooth vector field. We present a new and more conceptual proof of such result using the Jordan-Chevalley decomposition in algebraic groups and the properties of the exponential operator.We characterize the hyperbolic smooth (resp. formal) diffeomorphisms that are embedded in a smooth (resp. formal) flow. We introduce a criterion showing that the presence of weak resonances for a diffeomorphism plus two natural conditions imply that it is not embeddable. This solves a conjecture of Zhang. The criterion is optimal, we provide a method to construct embeddable diffeomorphisms with weak resonances if we remove any of the conditions. 相似文献
15.
H. Ninomiya H. F. Weinberger 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):869-873
We present an example of a predator-prey-like system
with a prey-only state as a global attractor, and with the
additional property that an attempt to control the prey by
harvesting or poisoning both species produces solutions in which
both populations blow up in finite time. 相似文献
16.
Begoña Alarcón Víctor GuíñezCarlos Gutierrez 《Nonlinear Analysis: Theory, Methods & Applications》2008
We consider sufficient conditions which guarantee that an embedding from the plane R2 into itself has a unique fixed point. We subsequently study sufficient conditions under which there appears a globally attracting fixed point for such an embedding. 相似文献
17.
In this work, we consider a new approach to the practical stability theory of impulsive functional differential equations. With Lyapunov functionals and Razumikhin technique, we use a new technique in the division of Lyapunov functions, given by Shunian Zhang, and obtain conditions sufficient for the uniform practical (asymptotical) stability of impulsive delay differential equations. An example is also discussed to illustrate the advantage of the proposed results. 相似文献
18.
In this paper we present a sufficient condition for the stability of the equilibrium of a nonlinear planar system. The proof is based on the computation of the corresponding Birkhoff normal forms. The result does not involve small parameters. Applications to the relativistic oscillator are also given. 相似文献
19.
In this paper, we get the existence of periodic and homoclinic solutions for a class of asymptotically linear or sublinear Hamiltonian systems with impulsive conditions via variational methods. However, without impulses, there is no homoclinic or periodic solution for the system considered in this paper. Moreover, our results can be used to study the existence of periodic and homoclinic solutions of difference equations. 相似文献
20.
A stage-structured predator–prey system with delays for prey and predator, respectively, is proposed and analyzed. Mathematical analysis of the model equations with regard to boundedness of solutions, permanence and stability are analyzed. Some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium, respectively, are obtained. 相似文献