Saddle-node bifurcation

Stability (learning theory)

Combinatorics

Machine learning

Physics

Mathematical analysis

Function (biology)

Artificial intelligence

Nonlinear system

Hopf bifurcation

Biological applications of bifurcation theory

Topology (electrical circuits)

Period-doubling bifurcation

Control (management)

Bifurcation

Applied mathematics

Mathematics

Computer science

Control theory (sociology)

Artificial neural network

Quantum mechanics

Center manifold

Evolutionary biology

Bifurcation diagram

Biology

Applied Mathematics and Computation

In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results.

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays