Almost Anti-periodic Solution of Inertial Neural Networks with Leakage and Time-Varying Delays on Timescales

This paper studies a class of inertial neural networks with leakages and varying delays on timescales: x(i) (Delta Delta) (t) = -a(i) (t)x(i)(Delta) (t-eta i (t)) - b(i) (t)x(i) (t-xi(i) (t)) + Sigma(j=1) (n) c(i j) (t) f(j) (x(j) (t)) + Sigma(j=1) (n)d(i j) (t)g(j) (x(j) (t - q(ij) (t))) + S-i (t). The problems of the existence, the uniqueness and the exponential stability of almost anti-periodic solution on timescales are investigated. We establish some sufficient conditions to guarantee the main results, by constructing the Lyapunov functions and using some classical inequalities. A numerical example is given for illustration.

Automated summary

This paper investigates a class of inertial neural networks with leakages and varying delays on timescales, focusing on the existence, uniqueness, and exponential stability of almost anti-periodic solutions. By constructing Lyapunov functions and applying classical inequalities, sufficient conditions are established to guarantee the main results. A numerical example is provided for illustration.