Stability (learning theory)

Machine learning

Physics

Macroeconomics

Artificial intelligence

Nonlinear system

Economics

Control (management)

Leakage (economics)

Bifurcation

Mathematics

Computer science

Control theory (sociology)

Artificial neural network

Quantum mechanics

Bifurcation theory

Chaos Solitons & Fractals

Recently, the dynamics of the fractional delayed neural networks has been considerably concerned. It is illustrated that time delay has a remarkable influence on the dynamical behaviors of the fractional neural networks. Nevertheless, the results of the fractional neural network with leakage delay are extremely few. It is the first time that the stability and bifurcation of fractional BAM neural networks with time delay in leakage terms is examined in the current paper. The stability criterion and the conditions of bifurcation are obtained for the proposed systems with or without leakage delay by selecting time delay as the bifurcation parameter. It is amazing that the leakage delay has a destabilizing influence on the stability performance of such system and they cannot be ignored. Moreover, the relation between the bifurcation point and the order is fully discussed by careful calculation. Finally, numerical examples are addressed to verify the feasibility of the obtained theoretical results.

New bifurcation results for fractional BAM neural network with leakage delay