Effect of Leakage Delays on Bifurcation in Fractional-Order Bidirectional Associative Memory Neural Networks with Five Neurons and Discrete Delays

Kosko B. Adaptive bi-directional associative memories. Appl Opt. 1987;26:4947–60.

Article  Google Scholar 

Cao JD, Zhou DM. Stability analysis of delayed cellular neural networks. Neural Netw. 1998;11:1601–5.

Article  Google Scholar 

Cao JD, Wang L. Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw. 2002;13(2):457–63.

Article  Google Scholar 

Cao JD, Liang JL, James J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D. 2004;199(3–4):425–36.

Article  MathSciNet  Google Scholar 

Cao JD, Song QK. Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity. 2006;19:1601–17.

Article  MathSciNet  Google Scholar 

Cao JD, Xiao M. Stability and Hopf bifurcation in a simplified BAM neural network with two time delays. IEEE Trans Neural Netw. 2007;18(2):416–30.

Article  Google Scholar 

Zhou FY, Ma CR. Global exponential stability of high-order BAM neural networks with reaction-diffusion terms. Int J Bifurcat Chaos. 2010;20(10):3209–23.

Article  MathSciNet  Google Scholar 

Wang BX, Jian JG. Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with distributed delays. Commun Nonlinear Sci Numer Simulat. 2010;15:189–204.

Article  MathSciNet  Google Scholar 

Wu HX, Liao XF, Feng W, Guo ST. Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays. Cogn Neurodyn. 2021;6:443–58.

Article  Google Scholar 

Wang TY, Zhu QX. Stability analysis of stochastic BAM neural networks with reaction-diffusion, multi-proportional and distributed delays. Physica A. 2019;533:121935.

Article  MathSciNet  Google Scholar 

Tao BB, Xiao M, Zheng WX, Cao JD. Dynamics analysis and design for a bidirectional super-ring-shaped neural network with \(n\) neurons and multiple delays. IEEE Trans Neural Netw Learn Syst. 2021;32:2978–92.

Article  MathSciNet  Google Scholar 

Nicolis JS. Chaos and Information Processing. Singapore: World Scientific; 1991.

Book  Google Scholar 

Shilnikov AL, Cymbalyuk GS. Transition between Tonio-spiking and bursting in a neuron model via the blue-sky catastrophe. Phys Rev Lett. 2005;94(4):048101.

Yu WW, Cao JD. Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays. Phys Lett A. 2006;351:64–78.

Article  Google Scholar 

Xu CJ, Zhang QM, Wu YS. Bifurcation analysis for two-neuron networks with discrete and distributed delays. Cogn Comput. 2016;8(6):1103–18.

Article  Google Scholar 

Javidmanesh E, Dadi Z, Afsharnezhad Z. Existence and Stability Analysis of Bifurcating Periodic Solutions in a Delayed Five-Neuron BAM Neural Network Model. Nonlinear Dyn. 2013;72(1):149–64.

Article  MathSciNet  Google Scholar 

Javidmanesh E, Dadi Z, Afsharnezhad Z, Effati S. Global stability analysis and existence of periodic solutions in an eight-neuron BAM neural network model with delays. J Intell Fuzzy Syst. 2014;27:391–406.

Article  MathSciNet  Google Scholar 

Liu YW, Li SS, Liu ZR, Wang RQ. High codimensional bifurcation analysis to a six-neuron BAM neural network. Cogn Neurodyn. 2016;10:149–64.

Article  Google Scholar 

Hilfer R. Applications of fractional calculus in physics. Singapore: World Scientific York; 2000.

Magin R. Fractional calculus in bioengineering. Crit Rev Biomed Eng. 2004;32(1):1–104.

Article  Google Scholar 

Kibas AA, Srivastava HM, Trujillo JJ. Theory and application of fractional differential equations. New York: Elsevier; 2006.

Google Scholar 

Zhang JM, Wu JW, Bao HB, Cao JD. Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays. Appl Math Comput. 2018;339:441–50.

MathSciNet  Google Scholar 

Shafiya M, Nagamani G, Dafik D. Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality. Math Comput Simulat. 2022;191:168–86.

Article  MathSciNet  Google Scholar 

Bao HB, Ju HP, Cao JD. Non-fragile state estimation for fractional-order delayed memristive BAM neural networks. Neural Netw. 2019;119:190–9.

Article  Google Scholar 

Nagamani G, Shafiya M, Soundararajan G, Prakash M. Robust state estimation for fractional-order delayed BAM neural networks via LMI approach. J Franklin Inst. 2020;357:4964–82.

Article  MathSciNet  Google Scholar 

Wu AL, Zeng ZG, Song XG. Global Mittag-Leffler stabilization of fractional-order bidirectional associative memory neural networks. Neurocomputing. 2016;177:489–96.

Xu CJ, Aouiti C, Liu ZX. A further study on bifurcation for fractional order BAM neural networks with multiple delays. Neurocomputing. 2020;417:501–15.

Article  Google Scholar 

Xu CJ, Liao MX, Li PL, Guo Y, Liu ZX. Bifurcation Properties for fractional order delayed BAM neural networks. Cogn Comput. 2021;13:322–56.

Article  Google Scholar 

Huang CD, Meng YJ, Cao JD, Alsaedi A, Alsaadi FE. New bifurcation results for fractional BAM neural network with leakage delay. Chaos, Solitons Fractals. 2017;100:31–44.

Article  MathSciNet  Google Scholar 

Huang CD, Liu H, Chen YF, Chen XP, Song F. Dynamics of a fractional-order BAM neural network with leakage delay and communication delay. Fractals. 2021;29(3):2150073.

Article  Google Scholar 

Gopalsamy K. Leakage delays in BAM. J Math Anal Appl. 2007;325(15):1117–32.

Article  MathSciNet  Google Scholar 

Tehrani NF, Razvan MR. Bifurcation structure of two coupled FHN neurons with delay. Math Biosci. 2015;270:41–56.

Article  MathSciNet  Google Scholar 

Podlubny I. Fractional differential equations. New York: Academic Press; 1999.

Google Scholar 

Bandyopadhyay B, Kamal S. Stabilization and control of fractional order systems: a sliding mode approach. Lecture Notes Electr Eng. 2015;317:115–27.

Article  MathSciNet  Google Scholar 

Matignon D. Stability results for fractional differential equations with applications to control processing. Computat Eng Syst Appl. 1996;2:963–8.

Google Scholar 

Fan DJ, Wei JJ. Hopf bifurcation analysis in a tri-neuron network with time delay. Nonlinear Anal RWA. 2008;9:9–25.

Article  MathSciNet  Google Scholar 

Comments (0)

No login
gif