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The optimization performance of transiently chaotic neural network (TCNN) is affected by various factors such as chaotic characteristic, model parameters, and annealing function, and its capacity of global optimization is limited. It is demonstrated that the non-monotonic activation function can generate richer chaotic characteristic than the monotonic activation function in the TCNN model. Besides, the activation function involving neurobiological mechanism can not only reflect the rich brain activity in brain waves, but also enhance the non-linear dynamic characteristic, which may further improve the global optimization ability. Hence, a novel chaotic neuron model is proposed with the non-monotonic activation function based on the neurobiological mechanisms from the electroencephalogram. The electroencephalogram consists of five brain waves (i.e., , , , , and waves) which are defined by the quality and intensity of brain waves with different frequency bands ranging from 0.5 Hz to 100 Hz. The brain wave with a higher frequency and a lower amplitude represents a more active brain. Researches demonstrate that the five brain waves can be simplified into sinusoidal waves with different frequencies. Hence, a frequency conversion sinusoidal (FCS) function which has the consistent frequency range and features with brain waves is designed based on the above neurobiological mechanisms. Then a novel chaotic neuron model with non-monotonic activation function which is composed of the FCS function and sigmoid function, is proposed for richer chaotic dynamic characteristic. The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed, indicating that the proposed FCS neuron model owns richer chaotic dynamic characteristic than transiently chaotic neuron model due to its special non-monotonic activation function. Based on the neuron model, a novel transiently-chaotic neural networkfrequency conversion sinusoidal chaotic neural network (FCSCNN) is constructed and the basis of model parameter selection is provided as well. To validate the effectiveness of the proposed model, the FCSCNN is applied to nonlinear function optimization and 10-city, 30-city, 75-city traveling salesman problem. The experimental results show that 1) the FCSCNN has a good performance under the condition of moderate a, smaller cA(0) and 2(0); 2) on the basis of the appropriate model parameters, the FCSCNN has better global optimization ability and optimization accuracy than Hopfield neural network, TCNN, improved-TCNN due to its richer chaotic characteristic in complicated combinational optimization problem, especially in middle and large scale problem.
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Keywords:
- chaotic neural network /
- electroencephalogram /
- frequency conversion sinusoidal chaotic neural network /
- combination optimization
[1] Han G, Qiao J F, Han H G, Chai W 2014 J. Control Decis. 29 2085 (in Chinese) [韩广, 乔俊飞, 韩红桂, 柴伟 2014 控制与决策 29 2085]
[2] Yu S J, Huan R S, Zhang J, Feng D 2014 Acta Phys. Sin. 63 060701 (in Chinese) [于舒娟, 宦如松, 张昀, 冯迪 2014 63 060701]
[3] Aihara K, Takabe T, Toyoda M 1990 Phys. Lett. A 144 333
[4] Chen L N, Aihara K 1995 Neural Networks 8 6
[5] Shuai J W, Chen Z X, Liu R T, Wu B X 1996 Phys. Lett. A 221 311
[6] Potapov A, Ali M K 2000 Phys. Lett. A 277 310
[7] Xiu C B, Liu X D, Zhang Y H, Tang Y Y 2005 Acta Electron. Sin. 33 868 (in Chinese) [修春波, 刘向东, 张宇河, 唐运虞 2005 电子学报 33 868]
[8] Xu Y Q, Sun M 2008 Control Theory A 25 574 (in Chinese) [徐耀群, 孙明 2008 控制理论与应用 25 574]
[9] Yi Z, Xu G J, Qin X Z, Jia Z H 2011 Proc. Eng. 24 479
[10] Xu Y Q, Xu N, Liu L J 2012 Appl. Mech. Mater. 151 532
[11] Zhang J H, Xu Y Q 2009 Nat. Sci. 1 204
[12] Zhang Q H Y, Xie X P, Zhu P, Chen H P, He G G 2014 Commun. Nonlinear Sci. 19 2793
[13] Zhang X D, Zhu P, Xie X P 2013 Acta Phys. Sin. 62 210506 (in Chinese) [张旭东, 朱萍, 谢小平, 何国光 2013 62 210506]
[14] Sih G C, Tang K K 2012 Theor. Appl. Fract. Mec. 61 21
[15] Mirzaei A, Safabakhsh R 2009 Appl. Soft. Comput. 9 863
[16] Qin K 2010 Ph. D. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [秦科 2010 博士学位论文 (成都: 电子科技大学)]
[17] Zhao L, Sun M, Cheng J H, Xu Y Q 2009 IEEE Trans. Neural Networks 20 735
[18] Liu X D, Xiu C B 2007 Neurocomputing 70 2561
[19] Kwok T, Smith K A 1999 IEEE Trans. Neural Networks 10 978
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[1] Han G, Qiao J F, Han H G, Chai W 2014 J. Control Decis. 29 2085 (in Chinese) [韩广, 乔俊飞, 韩红桂, 柴伟 2014 控制与决策 29 2085]
[2] Yu S J, Huan R S, Zhang J, Feng D 2014 Acta Phys. Sin. 63 060701 (in Chinese) [于舒娟, 宦如松, 张昀, 冯迪 2014 63 060701]
[3] Aihara K, Takabe T, Toyoda M 1990 Phys. Lett. A 144 333
[4] Chen L N, Aihara K 1995 Neural Networks 8 6
[5] Shuai J W, Chen Z X, Liu R T, Wu B X 1996 Phys. Lett. A 221 311
[6] Potapov A, Ali M K 2000 Phys. Lett. A 277 310
[7] Xiu C B, Liu X D, Zhang Y H, Tang Y Y 2005 Acta Electron. Sin. 33 868 (in Chinese) [修春波, 刘向东, 张宇河, 唐运虞 2005 电子学报 33 868]
[8] Xu Y Q, Sun M 2008 Control Theory A 25 574 (in Chinese) [徐耀群, 孙明 2008 控制理论与应用 25 574]
[9] Yi Z, Xu G J, Qin X Z, Jia Z H 2011 Proc. Eng. 24 479
[10] Xu Y Q, Xu N, Liu L J 2012 Appl. Mech. Mater. 151 532
[11] Zhang J H, Xu Y Q 2009 Nat. Sci. 1 204
[12] Zhang Q H Y, Xie X P, Zhu P, Chen H P, He G G 2014 Commun. Nonlinear Sci. 19 2793
[13] Zhang X D, Zhu P, Xie X P 2013 Acta Phys. Sin. 62 210506 (in Chinese) [张旭东, 朱萍, 谢小平, 何国光 2013 62 210506]
[14] Sih G C, Tang K K 2012 Theor. Appl. Fract. Mec. 61 21
[15] Mirzaei A, Safabakhsh R 2009 Appl. Soft. Comput. 9 863
[16] Qin K 2010 Ph. D. Dissertation (Chengdu: University of Electronic Science and Technology of China) (in Chinese) [秦科 2010 博士学位论文 (成都: 电子科技大学)]
[17] Zhao L, Sun M, Cheng J H, Xu Y Q 2009 IEEE Trans. Neural Networks 20 735
[18] Liu X D, Xiu C B 2007 Neurocomputing 70 2561
[19] Kwok T, Smith K A 1999 IEEE Trans. Neural Networks 10 978
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