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In this paper, logistic mapping with a time-dependent system-parameter (referred as "LMTD") is proposed. In various choices of time dependence, the periodic one has been tried in order to investigate the dynamical properties of LMTD. In certain parameter regions, two different attractors coexist depending on the initial values, for instances, two different chaotic attractors, two different periodic attractors, or two periodic/chaotic attractors. In addition, the whole configuration space of the initial values forms basins of attractions of which structures indicate self-similarity.

Chaos identification can not only promote the development and perfection of chaos theory, but also help to find the factors that produce chaos in the considered system, and control or anti-control it. The 0–1 test for chaos is an effective method to detect chaos. In order to simulate the noise contaminated through its production, Gaussian, Exponential, and Uniform noises are added to Logistic mapping to form a new hybrid time series, respectively. The effects of noise types and levels on the modified 0–1 test for chaos are studied. By studying the effect of different types of noises on chaos index $D_{\mathrm{\text{c}}}^{\ast }(n)$, $K_{\mathrm{\text{corr}}}^{\ast }(c)$, and the change of $K_{\mathrm{\text{m.corr}}}^{\ast }(c)$ with amplitude $\alpha$, it can be seen that Uniform noise has the greatest effect on chaos identification. In addition, it is found that the effect of the noise types on chaos identification depends on the peak of the noisy time series, and the effect of the noise on chaos detection increases with the increase of the noisy time series peak. It is worth noting that the selection of amplitude $\alpha$ can improve the noise resistance of chaos identification. The noise resistance of the modified 0–1 test for chaos can be improved by adjusting the amplitude $\alpha$ of the parameters. With the continuous increase of noise contamination level, the effect on the modified 0–1 test for chaos detection results is gradually enhanced, so reducing the noise contamination level is the key to improving the accuracy of the modified 0–1 test for chaos. In addition, adjusting the amplitude $\alpha$ can also play a certain noise immunity effect, and when $\alpha =2$, the noise immunity is stronger on logistic mapping. Sample size $N$ up to $2000$ is sufficient, but amplitude $\omega$ has little effect on chaos identification.

Machine loading problem in flexible manufacturing system is considered as a vital pre-release decision. Loading problem is concerned with assignment of necessary operations of the selected jobs to various machines in an optimal manner to minimize system unbalance under technological constraints of limited tool slots and operation time. Such a problem is combinatorial in nature and found to be NP-hard; thus, finding the exact solutions is computationally intractable and becomes impractical as the problem size increases. To alleviate above limitations, a meta-heuristic approach based on particle swarm optimization (PSO) has been proposed in this paper to solve the machine loading problem. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast toward global optimum and hence reduce computational effort further. Twenty benchmark problems available in open literature have been solved using the proposed heuristic. Comparison between the results obtained by the proposed heuristic and the existing methods show that the results obtained are encouraging at significantly less computational effort.

To solve the problem of efficiently and securely transmitting perceptual hash values in speech perceptual hashing authentication systems, a transparent and robust audio reversible watermarking algorithm is proposed in this paper. This algorithm, which is based on phase coding improved by bipolar quantization, guarantees its security by Logistic mapping. Experimental results show that the proposed algorithm has good reversibility, transparency, robustness and security, and has better comprehensive properties.