Searching for Strange Attractor in Sliver Irregularity Series

The chaotic nonlinear time series method is applied to analyze the sliver irregularity in textile processing.Because it unifies the system's determinacy and randomness,it seems more adaptive to describe the sliver irregularity than conventional methods.Firstly,the chaos character,i.e.fractal dimension,positive Lyapunov exponent,and state space parameters,including time delay and reconstruction dimension,are calculated respectively.As a result,a positive Lyapunov exponent and a fractal dimension are obtained,which demonstrates that the system is chaotic in fact.Secondly,both local linear forecast and global forecast models based on the reconstructed state are adopted to predict a segment part of the sliver irregularity series,which proves the validity of this analysis.Therefore,the sliver irregularity series shows the evidence of chaotic phenomena,and thus laying the theoretical foundation for analyzing and modeling the sliver irregularity series by applying the chaos theory,and providing a new way to understand the complexity of the sliver irregularity much better.

Stochasticst ability and Hopf bifurcation analysis of a singular bio-economic model with stochastic fluctuations

In this paper,we study a class of singular stochastic bio-economic models described by differential-algebraic equations due to the influence of economic factors.Simplifying the model through a stochastic averaging method,we obtained a two-dimensional diffusion process of averaged amplitude and phase.Stochastic stability and Hopf bifurcations can be analytically determined based on the singular boundary theory of diffusion process,the Maximal Lyapunov exponent and the invariant measure theory.The critical value of the stochastic Hopf bifurcation parameter is obtained and the position of Hopf bifurcation drifting with the parameter increase is presented as a result.Practical example is presented to verify the effectiveness of the results.