Stability and Control of Fractional-Order Fuzzy Stochastic Clifford-Valued Neural Networks with Hybrid Markovian Switching, Cyber-Attacks, and Event-Triggered Multi-Agent Synchronization

Abstract

We develop a rigorous stability and control theory for a class of Caputo fractional-order, Takagi–Sugeno (T–S) fuzzy, Itô stochastic, Clifford-valued neural networks (FFSCNNs) operating as agents of a leader–following multi-agent system. The model simultaneously incorporates (i) a Clifford (geometric) algebra state space that unifies the real, complex, quaternion and higher hypercomplex settings; (ii) hybrid Markovian switching of the network mode; (iii) time-varying transmission delays; (iv) an Itô diffusion term; (v) randomly occurring deception (false-data-injection) cyber-attacks governed by a Bernoulli process; and (vi) a dynamic event-triggered communication scheme that transmits sampled information only when a state-dependent threshold is violated. Using a real-domain decomposition of the Clifford algebra, a generalized quadratic Lyapunov function together with the Aguila-Camacho-Duarte-Mermoud-Gallegos fractional inequality, and a stochastic fractional Halanay comparison principle, we establish four load-bearing results: (1) global existence and uniqueness of the mild solution in mean square; (2) a set of linear matrix inequality (LMI) conditions guaranteeing global mean-square Mittag–Leffler synchronization of every follower to the leader under attacks and event-triggered control; (3) a strictly positive lower bound on the inter-event times (exclusion of Zeno behavior) derived from the Hölder regularity of Caputo trajectories; and (4) an attack-robustness margin quantifying the maximal tolerable attack intensity. All proofs are given in full, with each invoked classical result stated precisely. A controlled synthetic experiment and a reproducible simulation protocol, with runnable code, are provided to test the theoretical hypotheses; every reported number is labeled as either produced by supplied code or explicitly illustrative. Genuine modeling limitations, in particular the delicate interaction between the Caputo derivative and the Itô calculus, are stated openly rather than concealed.