In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it su...In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.展开更多
Different from the solution/physical pump, biological pump and continental shelf pump of carbon cycle in oceans, a new pump named “surface microlayer (SML) pump” is developed based on data obtained from marine inves...Different from the solution/physical pump, biological pump and continental shelf pump of carbon cycle in oceans, a new pump named “surface microlayer (SML) pump” is developed based on data obtained from marine investigations and lab study. The SML pump has: (1) left-right dissymmetry of “pH-depth” curve; (2) the non-linearity of “concentration-depth” curve; and (3) difference of affect-ing confine of the SML pump. The issue of “source” or “sink” of atmospheric CO2 in the Yellow Sea and South China Sea is discussed.展开更多
文摘In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.
基金This work was supported by the Great Project of the National Natural Science Foundation of China (Grant No. 40490263)the National Natural Science Foundation of China (Grant Nos. 40076020, 40376022)+1 种基金 the research for the Doctoral Program for Higher Education (Grant No. 20030423007) the '973' National Basic Research Priorities Programme (Grant No. 2001CB409703).
文摘Different from the solution/physical pump, biological pump and continental shelf pump of carbon cycle in oceans, a new pump named “surface microlayer (SML) pump” is developed based on data obtained from marine investigations and lab study. The SML pump has: (1) left-right dissymmetry of “pH-depth” curve; (2) the non-linearity of “concentration-depth” curve; and (3) difference of affect-ing confine of the SML pump. The issue of “source” or “sink” of atmospheric CO2 in the Yellow Sea and South China Sea is discussed.
