Recently some extensions of the classical Darboux integrability theory to autonomous and non-autonomous polynomial vector fields have been done. The classical Darboux integrability theory and its recent extensions are based on the existence of algebraic invariant hypersurfaces. However the algebraicity of the invariant hypersurfaces is not necessary and the unique necessary condition is the alg...

The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapu...

In this paper, a class of non-autonomous neural networks with delays is considered. By using the properties of spectral radius of nonnegative matrix, two new integral inequalities are established. Based on the integral inequalities, some new sufficient conditions for the existence of quasi-invariant and attracting sets of the non-autonomous neural networks with delays are obtained. The framewor...

with the continuous development of the industrialization process, the countries all over the world gradually appeared lack of agricultural labor force and aging phenomenon, which was especially prominent in developed countries. however the agricultural robot with high operating efficiency, high qualities of work will play an increasingly important role in future agricultural production. robot n...

In this paper we give some sufficient conditions, which ensure the existence of pseudo almost periodic solutions to some classes of non-autonomous first-order partial neutral functional-differential with unbounded delay. c © 2006 Elsevier Ltd. All rights reserved.

In this paper, we give two sufficient conditions on the existence of periodic solutions of the non-autonomous Rayleigh equation of retarded type by using the coincidence degree theory.

This article provides sufficient conditions for the existence of periodic solutions with nonconstant sign in a family of polynomial, non-autonomous, first-order differential equations that arise as a generalization of the Abel equation of the second kind.

We consider an autonomous conservative second order system defined by a potential which admits a connected set Γ of critical points at level zero. We prove the existence of multiple periodic solutions of large period which are located near Γ.

We review results on the existence and the long term behaviour of non– autonomous linear evolution equations. Emphasis is put on recent results on the asymptotic behaviour using a semigroup approach.