This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.
The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.
In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis.
Zhengquan YANG Zhongxin LIU Zengqiang CHEN Zhuzhi YUAN
Conventional PI control encounters some problems when dealing with large lag process in the presence of parameter uncertainties.For the typical first-order process,an observerbased linear active disturbance rejection control(LADRC) scheme is presented to cope with the difficulties,and a reduced-order observer scheme is proposed further.Some quantitative dynamic results with regard to non-overshoot characteristics are obtained.Finally,the performance boundaries of LADRC and PI control are explicitly compared with each other,which shows that the former is more superior in most cases.
A novel immunization strategy called the random walk immunization strategy on scale-free networks is proposed.Different from other known immunization strategies,this strategy works as follows:a node is randomly chosen from the network.Starting from this node,randomly walk to one of its neighbor node;if the present node is not immunized,then immunize it and continue the random walk;otherwise go back to the previous node and randomly walk again.This process is repeated until a certain fraction of nodes is immunized.By theoretical analysis and numerical simulations,we found that this strategy is very effective in comparison with the other known immunization strategies.
