Analysis of Hopf–Hopf Interactions Induced by Multiple Delays for Inertial Hopfield Neural Models

The investigation of dynamic behaviors inertial neural networks depicted by second-order delayed differential equations has received considerable attention. Substantial research been performed on the transformed first-order using traditional variable substitution. However, there are few studies bifurcation dynamics direct analysis. In this paper, a multi-delay Hopfield system with couplings is considered. perturbation scheme and non-reduced order technique firstly combined into studying induced Hopf–Hopf singularity. This combination avoids tedious computation overcomes disadvantages variable-substitution reduced-order method. neighbor interaction points, interesting found plane self-connected delay coupled delay. Multiple delays can induce switching stable periodic oscillation coexistence. explicit expressions solutions obtained. validity theoretical results shown through consistency numerical simulations.