Bifurcation Mechanisation of a Fractional-Order Neural Network with Unequal Delays
- PDF / 1,033,889 Bytes
- 17 Pages / 439.37 x 666.142 pts Page_size
- 69 Downloads / 149 Views
Bifurcation Mechanisation of a Fractional-Order Neural Network with Unequal Delays Chengdai Huang1
· Jinde Cao2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The theme of bifurcation for a class of fractional-order neural networks (FONNs) with unique delay has been incalculably elucidated. It exhibits that multiple delays are capable of increasing the complicacy of realistic FONNs, but this has been insufficiently probed into. This paper attempts to conduct a research on the stability and bifurcation for a FONN with two unequal delays. By intercalating one delay and taking remnant delay as a bifurcation parameter, the incongruent critical values of diverse delays-induced bifurcations are exactly gained. Eventually, confirmation experiments are offered to endorse the procured theory. Keywords Unequal delays · Stability · Fractional order · Hopf bifurcation · Neural networks
1 Introduction The explorations on the theory and applications of neural networks (NNs) have been garnered intense concerns thanks to their generally authentic applications [1–7]. Currently, fractional calculus has been favorably drawn into NNs in virtue of the pinpoint characterization for the dynamic response of the actual systems. It is exposed that fractional differentiation is emerged into NNs which can efficiently handle formation [8]. Some delightful results and applications have been founded for FONNs, such as image encryption [9], network approximation [10]. Therefore, it is requisite to explore the dynamics of FONNs. There has been an immensely ever-increasing attention in the explorations of FONNs, and some important and meritorious results were obtained [11–15]. In [11], the lag synchronization for delayed fractional-order memristive NNs was reached by the aid of switching jumps mismatch, and the lag quasisynchronization conditions were further derived. Researchers have the ability to develop prospective dynamical properties of nonlinear systems via impelling Hopf bifurcation methodology [16–20]. It is generally known that the bifurcations of integer-order systems have been excessively discussed. On account of high
B
Chengdai Huang [email protected]
1
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
2
Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing 210096, China
123
C. Huang, J. Cao
accurateness of describing NNs with the help of fractional calculus in comparison with accustomed ones, numerous scholars have been overwhelmingly enchanted by the bifurcations of fractional-order systems, and numerous valuable results have been reported [21–28]. In [21], the authors investigated a fractional delayed predator–prey model with Holling type II functional response including prey refuge and diffusion, and it indicated that the stability domain can be extended under the fractional order compared with integer-order one. In [24], the bifurcation control of a delayed fractional eco-epidemiologica
Data Loading...
