Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1192-1204.
Previous Articles Next Articles
Global Exponential Periodicity of Complex-Valued Neural Networks with Discontinuous Activation Functions
Yao Zou1(
),Chunna Zeng2(),Jin Hu1,*()
- 1 School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074
2 School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
-
Received:2018-10-31Online:2019-10-26Published:2019-11-08 -
Contact:Jin Hu E-mail:18323190385@163.com;zengchn@163.com;jhu@cqjtu.edu.cn -
Supported by:the NSFC(61773004);the NSFC(11801048);the Program of Chongqing Innovation Team Project in University(CXTDX201601022);the Natural Scinece Foundation Project of CQ CSTC(cstc2017jcyjAX0172);the Natural Scinece Foundation Project of CQ CSTC(cstc2017jcyjAX0022);the Natural Scinece Foundation Project of CQ CSTC(cstc2017jcyjAX0082);the Natural Scinece Foundation Project of CQ CSTC(cstc2018jcyjAX0606);the Technology Research Foundation of Chongqing Educational Committee(KJ1705118);the Technology Research Foundation of Chongqing Educational Committee(KJQN201800740);the Venture & Innovation Support Program for Chongqing Overseas Returnees(cx2018034)
CLC Number:
- O175.13
Cite this article
Yao Zou,Chunna Zeng,Jin Hu. Global Exponential Periodicity of Complex-Valued Neural Networks with Discontinuous Activation Functions[J].Acta mathematica scientia,Series A, 2019, 39(5): 1192-1204.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
"
"
| 1 |
Nitta T . Solving the XOR problem and the detection of symmetry using a single complex-valued neuron. Neural Networks, 2003, 16 (8): 1101- 1105
doi: 10.1016/S0893-6080(03)00168-0 |
| 2 |
Forti M , Nistri P . Global convergence of neural networks with discontinuous neuron activations. IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Applications, 2003, 50 (11): 1421- 1435
doi: 10.1109/TCSI.2003.818614 |
| 3 |
Lu W , Chen T . Dynamical behaviors of delayed neural network systems with discontinuous activation functions. Neural Computation, 2006, 18: 683- 708
doi: 10.1162/neco.2006.18.3.683 |
| 4 |
Li L , Huang L . Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations. Applied Mathematical Modelling, 2009, 33 (12): 4326- 4336
doi: 10.1016/j.apm.2009.03.014 |
| 5 |
Meng Y , Huang L , Guo Z , Hu Q . Stability analysis of Cohen-Grossberg neural networks with discontinuous neuron activations. Applied Mathematical Modelling, 2010, 34 (2): 358- 365
doi: 10.1016/j.apm.2009.04.016 |
| 6 |
Huang L , Wang J , Zhou X . Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations. Nonlinear Analysis:Real World Applications, 2009, 10 (3): 1651- 1661
doi: 10.1016/j.nonrwa.2008.02.022 |
| 7 |
Wang D , Huang L . Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays. Neural Networks, 2014, 51: 80- 95
doi: 10.1016/j.neunet.2013.12.005 |
| 8 |
Qin S , Cheng Q , Chen G . Global exponential stability of uncertain neural networks with discontinuous Lurie-type activation and mixed delays. Neurocomputing, 2016, 198: 12- 19
doi: 10.1016/j.neucom.2015.07.147 |
| 9 |
Bao G , Zeng Z . Global asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functions. Neurocomputing, 2016, 193: 242- 249
doi: 10.1016/j.neucom.2016.02.017 |
| 10 |
Zhou W , Zurada J M . Discrete-time recurrent neural networks with complex-valued linear threshold neurons. IEEE Transactions on Circuits and Systems Ⅱ:Express Briefs, 2009, 56 (8): 669- 673
doi: 10.1109/TCSII.2009.2025625 |
| 11 | Hirose A . Complex-Valued Neural Networks. Heidelberg: Springer, 2006 |
| 12 |
Hu J , Wang J . Global stability of complex-valued recurrent neural networks with time-delays. IEEE Transcations on Neural Networks and Learning Systems, 2012, 23 (6): 853- 865
doi: 10.1109/TNNLS.2012.2195028 |
| 13 |
Chen X , Song Q . Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing, 2013, 121: 254- 264
doi: 10.1016/j.neucom.2013.04.040 |
| 14 |
Hu J , Wang J . Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays. Neural Networks, 2015, 66: 119- 130
doi: 10.1016/j.neunet.2015.03.001 |
| 15 | Liu X , Chen T . Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Transactions on Neural Networks and Learning Systems, 2015, 27 (3): 593- 606 |
| 16 |
Chen X , Zhao Z , Song Q , Hu J . Multistability of complex-valued neural networks with time-varying delays. Applied Mathematics and Computation, 2017, 294: 18- 35
doi: 10.1016/j.amc.2016.08.054 |
| 17 |
Wang Z , Guo Z , Huang L , Liu X . Dynamical behavior of complex-valued hopfield neural networks with discontinuous activation functions. Neural Processing Letters, 2017, 45 (3): 1039- 1061
doi: 10.1007/s11063-016-9563-5 |
| 18 |
Gronwall T H . Note on the derivative with respect to a parameter of the solutions of a system of differential equations. Annals of Math, 1919, 20: 292- 296
doi: 10.2307/1967124 |
| 19 |
Bellman R . The stability of solutions of linear differential equations. Duke Mathematical Journal, 1943, 10: 643- 647
doi: 10.1215/S0012-7094-43-01059-2 |
| 20 | Filippov A . Differential Equations with Discontinuous Right-Hand Side. Boston: Kluwer Academic, 1998 |
| [1] | Tu Kun, Ding Huisheng. Shadowing Properties of Semilinear Nonautonomous Evolution Equations on Banach Spaces [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1144-1160. |
| [2] | Ren Hongyue, Zhou Liqun. Mean Square Exponential Synchronization of a Class of Proportional Delay Stochastic Neural Networks and Its Application [J]. Acta mathematica scientia,Series A, 2025, 45(3): 888-901. |
| [3] | Qiu Yangcong, Wang Qiru. Hyers-Ulam-Rassias Stability of First-Order Nonlinear Dynamic Equations on Time Scales [J]. Acta mathematica scientia,Series A, 2024, 44(2): 465-475. |
| [4] | Li Dan,Wei Fengying,Mao Xuerong. Survival Analysis of an SVIR Epidemic Model with Media Coverage [J]. Acta mathematica scientia,Series A, 2023, 43(5): 1595-1606. |
| [5] | Yingjie Fu,Guijie Lan,Shuwen Zhang,Chunjin Wei. Dynamics of a Stochastic Predator-Prey Model with Pulse Input in a Polluted Environment [J]. Acta mathematica scientia,Series A, 2019, 39(3): 674-688. |
| [6] | Li Zhouhong, Zhang Fengshuo, Cao Jinde, Alsaedi Ahmed, Alsaadi Fuad E. Almost Periodic Solution for a Non-Autonomous Two Species Competitive System with Feedback Controls on Time Scales [J]. Acta mathematica scientia,Series A, 2017, 37(4): 730-750. |
| [7] | Deng Jiqin, Deng Ziming. Existence and Uniqueness of Solutions for Nonlocal Cauchy Problem for Fractional Evolution Equations [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1157-1164. |
|