A novel non-Lyapunov approach through artificial bee colony algorithm for detecting unstable periodic orbits with high orders |
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| Authors: | Fei Gao Feng-xia Fei Yan-fang Deng Yi-bo Qi Balasingham Ilangko |
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| Affiliation: | 1. Department of Mathematics, School of Science, Wuhan University of Technology, Luoshi Road, 122 Wuhan, Hubei 430070, People’s Republic of China;2. Signal Processing Group, Department of Electronics and Telecommunications, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;3. Intervention Center, Oslo University Hospital, 0424 Oslo, Norway;4. Institute of Clinical Medicine, University of Oslo, 0316 Oslo, Norway;1. Faculty of Science and Technology, Keio University, Japan;2. Institute of Engineering Mechanics and Systems, University of Tsukuba, Japan;1. Department of Medicine, St. Michael''s Hospital, Toronto, Ontario, Canada;2. Department of Medicine, University of Toronto, Toronto, Ontario, Canada;3. Canadian Heart Research Centre, Toronto, Ontario, Canada;4. Department of Nephrology, Humber River Hospital, Toronto, Ontario, Canada;5. Department of Pharmacy, Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada;6. Department of Clinical Neurosciences, Hotchkiss Brain Institute, University of Calgary, Calgary, Alberta, Canada;7. Department of Radiology, Hotchkiss Brain Institute, University of Calgary, Calgary, Alberta, Canada;8. Department of Medicine, McGill University Health Centre, Hôpital Sacré Coeur de Montréal, Montréal, Quebec, Canada;9. Department of Medicine, University of Ottawa Heart Institute, Ottawa, Ontario, Canada;10. Department of Medicine, Université de Montréal, Institut de Cardiologie de Montréal, Montréal, Quebec, Canada;11. Department of Medicine, Thrombosis and Atherosclerosis Research Institute, McMaster University, Juravinski Henderson Hospital, Hamilton, Ontario, Canada;12. Department of Medicine, St. Paul''s Hospital, University of British Columbia, Vancouver, British Columbia, Canada;13. Department of Medicine, Western University, London, Ontario, Canada;14. Calgary Foothills Primary Care Network, Calgary, Alberta, Canada;1. Department of Electrical Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran;2. Department of Electrical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran;1. Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China;2. National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China;3. School of Automation Science and Electrical Engineering, Beihang University, 100191 Beijing, China |
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| Abstract: | In this paper, a novel non-Lyapunov way is proposed to detect the unstable periodic orbits (UPOs) with high orders by a new artificial bee colony algorithm (ABC). And UPOs with high orders of nonlinear systems, are one of the most challenging problems of nonlinear science in both numerical computations and experimental measures. The proposed method maintains an effective searching mechanism with fine equilibrium between exploitation and exploration. To improve the performance for the optimums of the multi-model functions and to avoid the coincidences among the UPOs with different orders, we add the techniques as function stretching, deflecting and repulsion to ABC. The problems of detecting the UPOs are converted into a non-negative functions’ minimization through a proper translation, which finds a UPO such that the objective function is minimized. Experiments to different high orders UPOs of 5 wellknown and widely used nonlinear maps indicate that the proposed algorithm is robust, by comparison of results through the ABC and quantum-behaved particle swarm optimization (QPSO), respectively. And it is effective even in cases where the Newton-family algorithms may not be applicable. Density of the orbits are discussed. Simulation results show that ABC is superior to QPSO, and it is a successful method in detecting the UPOs, with the advantages of fast convergence, high precision and robustness. |
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