Xu, Daolin; Li, Zhigang; Bishop, Steven R. Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. (English) Zbl 0996.37075 Chaos 11, No. 3, 439-442 (2001). Summary: The scaling factor characterizes the synchronized dynamics of projective synchronization in partially linear chaotic systems but it is difficult to be estimated. To manipulate projective synchronization of chaotic systems in a favored way, a control algorithm is introduced to direct the scaling factor onto a desired value. The control approach is derived from the Lyapunov stability theory. It allows us to arbitrarily amplify or reduce the scale of the response of the slave system via a feedback control on the master system. In numerical experiments, we illustrate the application to the Lorenz system. Cited in 32 Documents MSC: 37M05 Simulation of dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 34C60 Qualitative investigation and simulation of ordinary differential equation models PDFBibTeX XMLCite \textit{D. Xu} et al., Chaos 11, No. 3, 439--442 (2001; Zbl 0996.37075) Full Text: DOI References: [1] DOI: 10.1103/PhysRevE.54.3204 [2] DOI: 10.1103/PhysRevE.54.3204 [3] DOI: 10.1103/PhysRevE.54.3204 [4] DOI: 10.1103/PhysRevE.54.3204 [5] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 [6] DOI: 10.1103/PhysRevLett.74.1736 [7] DOI: 10.1103/PhysRevLett.74.1736 [8] DOI: 10.1103/PhysRevLett.81.1401 [9] DOI: 10.1103/PhysRevLett.81.321 [10] DOI: 10.1103/PhysRevLett.81.321 [11] DOI: 10.1142/S0218127492000823 · Zbl 0875.94134 [12] DOI: 10.1142/S0218127492000823 · Zbl 0875.94134 [13] DOI: 10.1103/PhysRevLett.74.1970 [14] DOI: 10.1103/PhysRevLett.74.1970 [15] DOI: 10.1103/PhysRevLett.74.1970 [16] DOI: 10.1103/PhysRevLett.74.1970 [17] DOI: 10.1016/S0375-9601(97)00187-4 · Zbl 1043.37502 [18] DOI: 10.1016/S0375-9601(97)00187-4 · Zbl 1043.37502 [19] DOI: 10.1016/S0375-9601(97)00187-4 · Zbl 1043.37502 [20] DOI: 10.1016/S0167-2789(96)00301-6 · Zbl 0898.70015 [21] DOI: 10.1016/S0167-2789(96)00301-6 · Zbl 0898.70015 [22] DOI: 10.1103/PhysRevLett.81.3639 [23] DOI: 10.1103/PhysRevLett.82.3042 [24] DOI: 10.1103/PhysRevE.63.027201 [25] DOI: 10.1016/S0375-9601(01)00185-2 · Zbl 0983.37036 [26] DOI: 10.1017/S0305004100033223 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.