This study constructs a novel four-dimensional fractional-order chaotic system. It verifies chaotic nonlinear dynamicbehaviors and physical reliability by numerical simulation and hardware circuit design. For a class of parameteruncertainty fractional different-lags ( τi ) chaotic systems, the authors design a time-delayed (δ) synchronization controllersand parameter adaptive laws. It proves that the drive system and the response system tend to be synchronized andidentified parameter when the control parameter matrix K satisfies the condition that K – nE is a positive definite matrix.Simulation results show physical reliability of the fractional-order different-lags chaotic system and verify effectivenessof different-lags synchronization in time-delayed system method design.
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