Quantum mechanics

Hopf bifurcation

Control (management)

Bifurcation

Applied mathematics

Prime (order theory)

Stability (learning theory)

Economics

Computer science

Saddle-node bifurcation

Biological applications of bifurcation theory

Physics

Nonlinear system

Period-doubling bifurcation

Mathematics

Mathematical analysis

Artificial intelligence

Combinatorics

Uniqueness

Finance

Bifurcation diagram

Control theory (sociology)

Artificial neural network

Order (exchange)

Machine learning

Communications in Nonlinear Science and Numerical Simulation

Delay has a vital influence on the dynamics of neural networks. Exploring the effect of time delay on the dynamics of neural networks has become a hot issue in mathematics and engineering fields. In this current manuscript, on the basis of the earlier publications, we put forward a new fractional-order 4D neural networks incorporating two different time delays. First of all, the existence and uniqueness, boundedness of the solution of the fractional-order 4D neural networks incorporating two different time delays. are analyzed by applying contraction mapping principle, construct of an adaptive function, respectively. Next, the stability and the emergence of Hopf bifurcation are explored by making use of the stability and bifurcation theory of fractional-order dynamical system. A series of novel stability criteria and bifurcation conditions guaranteeing the stability and the emergence of Hopf bifurcation of the considered fractional-order 4D neural networks under the different delay cases are built. What,s more, the impact of delay on stabilizing neural networks and controlling the emergence of Hopf bifurcation of neural networks is adequately uncovered. At last, Matlab simulation figures are presented to confirm scientificness of the derived prime conclusions. The derived prime conclusions of this manuscript are perfectly innovative and own momentous theoretical reference value in the control issue and design aspect of neural networks.

New insight into bifurcation of fractional-order 4D neural networks incorporating two different time delays