Chaotic Dynamics in a Fractional-Order Hopfield Neural Network and its Stabilization via an Adaptive Model-Free Control Method
نویسندگان
1 Electrical and Computer Engineering Department, University of Windsor, Windsor, ON, Canada
2 School of Economics and Statistics, Guangzhou University, P.O. Box. 510006, Guangzhou, China
3 School of Economics and Statistics, Guangzhou University, P.O. Box. 510006, Guangzhou, China
4 Department of Automation, Biomechanics and Mechatronics, Lods University of Technology, Poland
doi
10.30473/coam.2022.59941.1169چکیده
The present study introduces a kind of fractional-order Hopfield neural network (FOHNN), and its complex dynamic behavior is investigated through chaos analyses. With the use of phase space analysis and bifurcation diagrams and maximal Lyapunov exponent (MLE) it is demonstrated that for the values of 0.87 < α < 1, as the fractional-order (FO), the dynamical behavior of the mentioned FOHNN is chaotic. Then, the bounded trait of chaotic systems is utilized to derive an adaptive model-free control technique to suppress of complex dynamics of the FOHNN. Furthermore, according to the matrix analysis theorem of non-integer-order systems and the adaptive model-free control methodology, analytical consequences of the designed controller are evidenced. Eventually, two examples are reported to illustrate the applicability of the mentioned model-free control method.
