Abstract
In recent years, an extreme learning machine that has a simple structure and good generalization has been applied to various problems. We have applied this extreme learning machine to reconstruction of bifurcation diagrams (BDs). We have reconstructed the BDs of various systems using the extreme learning machine. However, we have noticed that the original extreme learning machine, whose range of the synaptic weights of hidden neurons is \(\left[ -1,1 \right] \), cannot predict time series of the chaotic neuron model, although it is important for the reconstruction of bifurcation diagram to predict time series of target systems. In this paper, we show that the extreme learning machine can predict time series of chaotic neuron models by adjusting the synaptic weights of hidden neurons. In addition, we reconstruct the BDs of chaotic neuron models.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Huang, G.B., Zhu, Q.Y., Siew, C.K.: Extreme learning machine: theory and applications. Neurocomputing 70, 489–501 (2006)
Itoh, Y., Tada, Y., Adachi, M.: Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine. NOLTA, IEICE 8(1), 2–14 (2017)
Tokunaga, R., Kajiwara, S., Matsumoto, S.: Reconstructing bifurcation diagrams only from time-waveforms. Physica D 79, 348–360 (1994)
Aihara, K., Takabe, T., Toyoda, M.: Chaotic neural networks. Phys. Lett. A 144(6), 333–340 (1990)
Itoh, Y., Adachi, M.: Reconstruction of bifurcation diagrams using an extreme learning machine with a pruning algorithm. In: 2017 International Joint Conference on Neural Networks (2017)
Itoh, Y., Adachi, M.: Reconstruction of bifurcation diagrams using time-series data generated by electronic circuits of the Rössler equations. In: 2017 International Symposium on Nonlinear Theory and its Applications, pp. 439–442 (2017)
Itoh, Y., Adachi, M.: Bifurcation diagrams in estimated parameter space using a pruned extreme learning machine. Phys. Rev. E 98, 013301 (2018)
Barlett, P.L.: For valid generalization, the size of the weights is more important than the size of the network. In: Mozer, M., Jordan, M., Petsche, T. (eds.) Advances in Neural Information Processing Systems’ 1996, vol. 9, pp. 134–140. MIT Press, Cambridge (1997)
Preisendorfer, R.W., Mobley, C.D.: Principal Component Analysis in Meteorology and Oceanography. Elsevier, Amsterdam (1988)
Shimada, I., Nagashima, T.: A numerical approach to ergodic problem of dissipative dynamical systems. Prog. Theor. Phys. 61(6), 1605–1616 (1979)
Sano, M., Sawada, Y.: Measurement of the Lyapunov spectrum from chaotic time series. Phys. Rev. Lett. 55, 1082 (1985)
Adachi, M., Kotani, M.: Identification of chaotic dynamical systems with back-propagation neural networks. IEICE Trans. Fundam. E77–A(1), 324–334 (1994)
Acknowledgments
This paper was supported by the NEC C&C Foundation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Itoh, Y., Adachi, M. (2020). Reconstructing Bifurcation Diagrams of a Chaotic Neuron Model Using an Extreme Learning Machine. In: Cao, J., Vong, C., Miche, Y., Lendasse, A. (eds) Proceedings of ELM 2018. ELM 2018. Proceedings in Adaptation, Learning and Optimization, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-23307-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-23307-5_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23306-8
Online ISBN: 978-3-030-23307-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)