Global attractivity of memristor-based fractional-order neural networks

Some dynamical properties, especially the global attractivity, of memristor-based fractional-order neural networks (FNN) are discussed. By using Filippov solutions, the existence of memristor-based FNN's solutions is firstly guaranteed under a growth condition. With non-Lipschitz neuron activations, different dynamics of memristor-based FNN are analyzed by employing the Lyapunov functionals. Then, a local Mittag-Leffler stability condition is presented for memristor-based FNN. To obtain the global dynamical properties, the global boundedness of memristor-based FNN is discussed. Further, with proposing additional conditions, the global attractivity of memristor-based FNN is realized. To verify the effectiveness of the obtained results, three numerical examples are given in the end.