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Projective and functional projective synchronizations in quaternion-valued inertial neural networks with interaction
Vaibhav Agrawal1, Ahindra Sarkar1, Subir Das1
1Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005, India.
Abstract:
This study addresses projective synchronization (PS) and function projective synchronization (FPS) in quaternion-valued inertial neural networks (QVINNs) with generalized delays. A generalized delay-based lemma is proposed to establish synchronization criteria. Effective controllers are designed to guarantee PS and FPS between the drive and response systems. Using one-norm technique, sufficient conditions are derived for the reduced system. Two main theorems, Theorems 1 and 2, are presented. Theorem 1 has employed a complex Lyapunov function in the non-reduced case, while the Theorem 2 has adopted a simpler one-norm-based Lyapunov approach. The proposed framework reduces computational complexity and simplifies the proof process. Additionally, an audio encryption scheme based on random permutation matrix and synchronization is developed, and the results are validated through numerical simulations, confirming the effectiveness of the proposed results.
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