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Turán's problem and Ramsey numbers for trees

Zhi-Hong SunLin-Lin WangYi-Li Wu — 2015

Colloquium Mathematicae

Let T¹ₙ = (V,E₁) and T²ₙ = (V,E₂) be the trees on n vertices with V = v , v , . . . , v n - 1 , E = v v , . . . , v v n - 3 , v n - 4 v n - 2 , v n - 3 v n - 1 and E = v v , . . . , v v n - 3 , v n - 3 v n - 2 , v n - 3 v n - 1 . For p ≥ n ≥ 5 we obtain explicit formulas for ex(p;T¹ₙ) and ex(p;T²ₙ), where ex(p;L) denotes the maximal number of edges in a graph of order p not containing L as a subgraph. Let r(G₁,G₂) be the Ramsey number of the two graphs G₁ and G₂. We also obtain some explicit formulas for r ( T , T i ) , where i ∈ 1,2 and Tₘ is a tree on m vertices with Δ(Tₘ) ≤ m - 3.

The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments

Lin Jun WangYou Xiang XieQi Cheng Deng — 2018

Kybernetika

In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed...

Stability analysis and absolute synchronization of a three-unit delayed neural network

Lin Jun WangYou Xiang XieZhou Chao WeiJian Peng — 2015

Kybernetika

In this paper, we consider a three-unit delayed neural network system, investigate the linear stability, and obtain some sufficient conditions ensuring the absolute synchronization of the system by the Lyapunov function. Numerical simulations show that the theoretically predicted results are in excellent agreement with the numerically observed behavior.

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