Weak center for a class of Λ–Ω differential systems

In this paper, we give the necessary and sufficient conditions for a class of higher degree polynomial systems to have a weak center. As corollaries, we prove the correctness of the two conjectures about the weak center problem for the Λ–Ω differential systems

On the analytic commutator for Λ–Ω differential systems

In this paper, we give the necessary and sufficient conditions for some Λ–Ω differential systems to have an analytic commutator, use these properties to judge the origin point of the Λ–Ω differential systems to be an isochronous center

On the composition conjecture for a class of rigid systems

In this paper, we prove that for a class of rigid systems the Composition Conjecture is correct. We show that the Moments Condition is the sufficient and necessary conditions for these rigid systems to have a center at origin point. By the obtained conclusions we can derive all the focal values of these higher order polynomial differential systems and their expressions are more succinct and beautiful

A New Method for Research on the Center-Focus Problem of Differential Systems

We will introduce Mironenko’s method to discuss the Poincaré center-focus problem, and compare the methods of Lyapunov and Mironenko. We apply the Mironenko method to discuss the qualitative behavior of solutions of some planar polynomial differential systems and derive the sufficient conditions for a critical point to be a center

The Research of Periodic Solutions of Time-Varying Differential Models

We have studied the periodicity of solutions of some nonlinear time-varying differential models by using the theory of reflecting functions. We have established a new relationship between the linear differential system and the Riccati equations and applied the obtained results to discuss the behavior of periodic solutions of the Riccati equations

On the composition conjecture for a class of rigid systems

In this paper, we prove that for a class of rigid systems the Composition Conjecture is correct. We show that the Moments Condition is the sufficient and necessary conditions for these rigid systems to have a center at origin point. By the obtained conclusions we can derive all the focal values of these higher order polynomial differential systems and their expressions are more succinct and beautiful