This paper is concerned with the problem of complex function projective synchronization for uncertain networked chaotic complex systems. Based on Lyapunov stability, an adaptive control method is proposed for complex modified projective synchronization, which guarantees that the general drive-response networked chaotic complex systems are synchronized up to a complex scaling function matrix. Moreover, a complex fuzzy logic-based observer is designed to compensate for the model uncertainties and the external disturbances that exist in response networks, without prior information about uncertain factors. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.
SmB 6 is a strongly correlated material that has been attributed as a topological insulator and a Kondo insulator. Recent studies have found the topological surface states and low temperature insulating character to be profoundly robust against magnetic and nonmagnetic impurities. Here, we use angle resolved photoemission spectroscopy to chart the evolution of topologically linked electronic structure features versus magnetic doping and temperature in Sm 1−x M x B 6 (M = Eu, Ce). Topological coherence phenomena are observed out to ∼30% Eu and 50% Ce concentrations that represent extreme nominal hole and electron doping, respectively. Theoretical analysis reveals that a recent redesignation of the topologically inverted band symmetries provides a natural route to reconciling the persistence of topological surface state emergence even as the insulating gap is lost through decoherence.
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