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Global matrix projective synchronization of delayed fractional-order neural networks

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Abstract

This paper extends the projection scaling factor to a general constant matrix and research the global matrix projection synchronization (GMPS) for the delayed fractional-order neural networks (DFONNs) by using the sliding mode controller (SMC). GMPS is far more complex and difficult than other general synchronization types, so it can enhance the strong confidentiality and high security. Firstly, for the DFONNs, the optimal sliding surface and SMC are constructed. Secondly, the sufficient condition for achieving GMPS is presented. Moreover, the error system’s reachability and stability are analyzed and proved, and the GMPS is realized well. At last, the trajectories of error system and GMPS of state variables for a three-dimensional example are simulated to verify the feasibility of synchronization theory analysis. Particularly, GMPS can be reduced to the complete synchronization, anti-synchronization, projective synchronization (PS) and modified PS. This research will expand the synchronization theory of fractional-order neural networks (FONNs) and gives a general method to realize the GMPS of other fractional-order systems.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant numbers (12102492) and (12172166)], Key Research Projects of Henan Higher Education Institutions [Grant number (22A110027)], Henan Postdoctoral Foundation [Grant number (202101013)], Major Scientific and Technological Innovation Projects of Shandong Province [Grant number (2019JZZY010111)] and the Key Research and Development Plan of Shandong Province [Grant number (2019GGX104092)].

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Authors and Affiliations

  1. College of Science, Zhongyuan University of Technology, Zhengzhou, 451191, People’s Republic of China

    Jin-Man He

  2. College of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450000, People’s Republic of China

    Jin-Man He

  3. School of Computer and Information Engineering, Qilu Institute of Technology, Jinan, 250200, People’s Republic of China

    Teng-Fei Lei

  4. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Fang-Qi Chen

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  1. Jin-Man He
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  2. Teng-Fei Lei
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  3. Fang-Qi Chen
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Contributions

J-M He was mainly responsible for theoretical and methodological innovation, calculation and writing the initial draft. F-Q Chen was mainly responsible for revising and proofreading papers. T-F Lei was mainly responsible for numerical simulation. All authors read and approved the final manuscript.

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Correspondence to Jin-Man He.

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He, JM., Lei, TF. & Chen, FQ. Global matrix projective synchronization of delayed fractional-order neural networks. Soft Comput 27, 8991–9000 (2023). https://doi.org/10.1007/s00500-023-07834-5

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