Stability and Hopf bifurcation for a quaternion-valued three-neuron neural network with leakage delay and communication delay

Abstract

This paper proposes the stability and Hopf bifurcation for a quaternion-valued neural network(QVNN) with leakage delay and communication delay. Due to the higher order of the characteristic equation, the order of characteristic equation is reduced via the matrix block theory. Simultaneously, taking the leakage delay and communication delay as bifurcation parameter respectively, a number of conditions ensuring the stability of Hopf bifurcation periodic solutions are established. It lavishly illustrates that the stability of QVNN can be demolished more when considering the leakage delay as bifurcation parameter. Finally one simulations example is given to validate the theoretical results.