Title of article :
Chaotic Dynamics in a Fractional-Order Hopfield Neural Network and its Stabilization via an Adaptive Model-Free Control Method
Author/Authors :
Roohi, Majid School of Economics and Statistics - Guangzhou University, Guangzhou, China , Pourmahmood Aghababa, Mohammad Electrical and Computer Engineering Department - University of Windsor, Windsor, ON, Canada , Ziaei, Javid Department of Automation - Biomechanics and Mechatronics - Lods University of Technology, Poland , Zhang, Chongqi School of Economics and Statistics - Guangzhou University, Guangzhou, China
Abstract :
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.
Keywords :
Fractional-order systems , Hopfield neural network , Bifurcation , Adaptive model-free controller , Stabilization
Journal title :
Control and Optimization in Applied Mathematics
