Wong, W. K.; Zhen, Bin; Xu, Jian; Wang, Zhijie An analytic criterion for generalized synchronization in unidirectionally coupled systems based on the auxiliary system approach. (English) Zbl 1319.34098 Chaos 22, No. 3, 033146, 8 p. (2012). Summary: An analytic criterion is developed to investigate generalized synchronization (GS) in unidirectionally coupled systems based on the auxiliary system approach. The criterion is derived by transforming the existence problem of generalized synchronization into an eigenvalue problem. Numerical simulations show that the analytic criterion is almost as accurate as the response Lyapunov exponents method, and may provide an estimation of the threshold of strong generalized synchronization. A significant result can be deduced from our analysis that the more the number of equilibria of the unidirectionally coupled systems, the greater the chance of generalized synchronization, but the harder it may be for strong generalized synchronization to occur.{©2012 American Institute of Physics} Cited in 4 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D06 Synchronization of solutions to ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations PDFBibTeX XMLCite \textit{W. K. Wong} et al., Chaos 22, No. 3, 033146, 8 p. (2012; Zbl 1319.34098) Full Text: DOI Link References: [1] DOI: 10.1017/CBO9780511755743 · doi:10.1017/CBO9780511755743 [2] DOI: 10.1007/978-3-540-71269-5 · Zbl 1137.37018 · doi:10.1007/978-3-540-71269-5 [3] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821 [4] DOI: 10.1103/PhysRevE.51.980 · doi:10.1103/PhysRevE.51.980 [5] DOI: 10.1103/PhysRevE.67.066218 · doi:10.1103/PhysRevE.67.066218 [6] DOI: 10.1103/PhysRevLett.76.1816 · doi:10.1103/PhysRevLett.76.1816 [7] DOI: 10.1103/PhysRevE.61.3716 · doi:10.1103/PhysRevE.61.3716 [8] DOI: 10.1063/1.3309017 · Zbl 1311.34114 · doi:10.1063/1.3309017 [9] Strogatz S. H., Nonlinear Dynamics and Chaos (1994) [10] DOI: 10.1103/PhysRevE.53.4528 · doi:10.1103/PhysRevE.53.4528 [11] DOI: 10.1016/S0167-2789(99)00140-2 · Zbl 0976.92011 · doi:10.1016/S0167-2789(99)00140-2 [12] DOI: 10.1103/PhysRevE.61.5142 · doi:10.1103/PhysRevE.61.5142 [13] DOI: 10.1209/0295-5075/87/50002 · doi:10.1209/0295-5075/87/50002 [14] DOI: 10.1103/PhysRevLett.80.3053 · Zbl 1122.34318 · doi:10.1103/PhysRevLett.80.3053 [15] DOI: 10.1103/PhysRevE.54.R4508 · doi:10.1103/PhysRevE.54.R4508 [16] DOI: 10.1103/PhysRevE.78.025205 · doi:10.1103/PhysRevE.78.025205 [17] DOI: 10.1103/PhysRevE.81.016208 · doi:10.1103/PhysRevE.81.016208 [18] DOI: 10.1103/PhysRevE.55.4029 · doi:10.1103/PhysRevE.55.4029 [19] DOI: 10.1063/1.2978180 · Zbl 1309.34093 · doi:10.1063/1.2978180 [20] DOI: 10.1103/PhysRevE.67.026223 · doi:10.1103/PhysRevE.67.026223 [21] DOI: 10.1142/S0218127499000092 · Zbl 0937.37019 · doi:10.1142/S0218127499000092 [22] S. Cincotti and A. Teglio, Proc. IEEE International Symposium on Circuits and Systems 2002 (ISCAS 2002), Vol. 3, pp. 61. [23] DOI: 10.1016/j.chaos.2003.12.024 · Zbl 1060.93531 · doi:10.1016/j.chaos.2003.12.024 [24] DOI: 10.1063/1.2903841 · Zbl 1307.34079 · doi:10.1063/1.2903841 [25] DOI: 10.1063/1.3076397 · Zbl 1311.34113 · doi:10.1063/1.3076397 [26] DOI: 10.1016/j.physa.2009.12.035 · doi:10.1016/j.physa.2009.12.035 [27] DOI: 10.1007/BFb0064319 · doi:10.1007/BFb0064319 [28] DOI: 10.1103/PhysRevE.71.067201 · doi:10.1103/PhysRevE.71.067201 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.