Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field |
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| Authors: | Anbalagan Pratap Ramachandran Raja Jehad Alzabut Jinde Cao Grienggrai Rajchakit Chuangxia Huang |
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| Affiliation: | 1. Department of Mathematics, Vel Tech High Tech Dr Rangarajan Dr Sakunthala Engineering College, Avadi, India;2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, India;3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;4. School of Mathematics, Southeast University, Nanjing, China;5. Department of Mathematics, Maejo University, Chiangmai, Thailand;6. School of Mathematics and Statistics, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, China |
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| Abstract: | Fractional order quaternion-valued neural networks are a type of fractional order neural networks for which neuron state, synaptic connection strengths, and neuron activation functions are quaternion. This paper is dealing with the Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. The fractional order quaternion-valued neural networks are separated into four real-valued systems forming an equivalent four real-valued fractional order neural networks, which decreases the computational complexity by avoiding the noncommutativity of quaternion multiplication. Via some fractional inequality techniques and suitable Lyapunov functional, a brand new criterion is proposed first to ensure the Mittag-Leffler stability for the addressed neural networks. Besides, the combination of quaternion-valued adaptive and impulsive control is intended to realize the asymptotically synchronization between two fractional order quaternion-valued neural networks. Ultimately, two numerical simulations are provided to check the accuracy and validity of our obtained theoretical results. |
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| Keywords: | adaptive and impulsive synchronization fractional order Mittag-Leffler stability quaternion-valued neural networks |
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