Fixed-time synchronization of clifford biquaternion neural networks with two-sided coefficients and application to multispectral image protection.

This paper introduces a Clifford biquaternion neural network (CBNN) with two-sided coefficients and investigates its fixed-time synchronization, along with an application to multispectral image protection. The proposed model offers a unified eight-dimensional hypercomplex representation and naturally captures the distinct left-right interactions arising from noncommutative multiplication. By decomposing the CBNN into four complex-subalgebra subsystems, we design a generalized complex sign-based controller and derive sufficient conditions for exact fixed-time synchronization of the continuous-time system, with an explicit upper bound that is independent of the initial synchronization error. Complementary exponential- and finite-time results are also provided to further elucidate the different convergence behaviors. Numerical experiments on two- and four-neuron CBNNs, including a fully deterministic nonuniform example, corroborate the theoretical findings. Under standard settings, the proposed controller attains the smallest numerical threshold-reaching time across all tested initial errors. In the context of multispectral image protection, the synchronized CBNN states are combined with a shared master key and a public nonce to generate permutation and hybrid modular-addition/XOR diffusion material. Experiments on an eight-band multispectral image confirm exact recovery under noiseless transmission, high ciphertext entropy, strong sensitivity to both key and plaintext, and robustness against impulsive noise.