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In this paper, the exponential synchronization of fractional-order multi-links complex dynamical networks (CDNs) is studied based on non-periodically intermittent control. By means of the Lyapunov method and graph-theoretic approach, a Lyapunov-type theorem is provided based on the existence of vertex-Lyapunov functions. Then by giving the specific vertex-Lyapunov functions, a coefficients-type theorem is presented where the conditions of it are based on the coefficients of system. Moreover, to show the practicality of theoretical results, we give two applications to fractional-order chaotic CDNs with multiple links and fractional-order Hindmarsh–Rose neuron systems with multiple links, respectively. Meanwhile, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results.

Non-periodically intermittent exponential synchronization of fractional-order multi-links complex dynamical networks