Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.
In opinion dynamics,the convergence of the heterogeneous Hegselmann-Krause(HK) dynamics has always been an open problem for years which looks forward to any essential progress.In this short note,we prove a partial convergence conclusion of the general heterogeneous HK dynamics.That is,there must be some agents who will reach static states in finite time,while the other opinions have to evolve between them with a minimum distance if all the opinions does not reach consensus.And this result leads to the convergence of several special cases of heterogeneous HK dynamics,including when the minimum confidence bound is large enough,the initial opinion difference is small enough,and so on.
We study the mean-square composite-rotating consensus problem of second-order multi-agent systems with communication noises, where all agents rotate around a common center and the center of rotation spins around a fixed point simultaneously. Firstly, a time-varying consensus gain is introduced to attenuate to the effect of communication noises. Secondly, sufficient conditions are obtained for achieving the mean-square composite-rotating consensus. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithm.
