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Drive network to a desired orbit by pinning control

Quanjun Wu, Hua Zhang (2015)

Kybernetika

The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays...

Dynamic analysis of an impulsive differential equation with time-varying delays

Ying Li, Yuanfu Shao (2014)

Applications of Mathematics

An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results.

Dynamic behavior of vector solutions of a class of 2-D neutral differential systems

Arun Kumar Tripathy, Shibanee Sahu (2025)

Mathematica Bohemica

This work deals with the analysis pertaining some dynamic behavior of vector solutions of first order two-dimensional neutral delay differential systems of the form d d t u ( t ) + p u ( t - τ ) v ( t ) + p v ( t - τ ) = a b c d u ( t - α ) v ( t - β ) . The effort has been made to study d d t x ( t ) - p ( t ) h 1 ( x ( t - τ ) ) y ( t ) - p ( t ) h 2 ( y ( t - τ ) ) + a ( t ) b ( t ) c ( t ) d ( t ) f 1 ( x ( t - α ) ) f 2 ( y ( t - β ) ) = 0 , where p , a , b , c , d , h 1 , h 2 , f 1 , f 2 C ( , ) ; α , β , τ + . We verify our results with the examples.

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

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