System Decomposition Method-Based Exponential Stability of Clifford-Valued BAM Delayed Neural Networks

This study explores new theoretical results for the global exponential stability of bidirectional associative memory delayed neural networks in the Clifford domain. By considering time-varying delays, a general class of Clifford-valued bidirectional associative memory neural networks is formulated, which encompasses real-, complex-, and quaternion-valued neural network models as special cases. To analyze the global exponential stability, we first decompose the considered
$n$
-dimensional Clifford-valued networks into
$2^{m}n$
-dimensional real-valued networks, which avoids the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers. Subsequently, we establish new sufficient conditions to guarantee the existence, uniqueness, and global exponential stability of equilibrium points for the considered networks by constructing a new Lyapunov functional and applying homeomorphism theory. Finally, we provide a numerical example accompanied by simulation results to illustrate the validity of the obtained theoretical results. The present results remain valid even when the considered neural networks degenerate into real-, complex-, and quaternion-valued networks.