A mathematical study published in Neural Processing Letters has resolved the global Mittag-Leffler synchronization problem for a class of complex-valued fractional-order memristor-based neural networks subjected to multiple delays. Researchers Suriguga Ma and Na Zhang investigated this mathematical class of complex dynamical networks under the simultaneous influence of both leakage delays and time-varying delays. By formulating explicit algebraic criteria, the authors demonstrated that drive and response network systems can achieve guaranteed global synchronization.
This reformulation was accomplished by separating the complex-valued states into their real and imaginary parts, while similarly decomposing the system activation functions into real and imaginary components. Furthermore, because memristor-based connection weights exhibit discontinuous switching dynamics, the researchers utilized Filippov’s differential inclusion theory to rigorously treat and accommodate the discontinuous connection weights within the real-valued framework.
Within this transformed real-valued analytical setting, the researchers designed and systematically analyzed two distinct control strategies to achieve synchronization: a state-feedback controller and an adaptive controller. To establish mathematical guarantees for global Mittag-Leffler synchronization, the study constructed fractional-order Lyapunov functionals and applied appropriate fractional inequalities. Through this analytical procedure, the authors derived explicit algebraic conditions that govern the synchronization process. The derived criteria provide precise mathematical benchmarks that ensure the response system synchronizes with the drive system under the defined leakage and time-varying delay conditions.
The adaptive controller offers enhanced flexibility because its gains are updated online and need not be prescribed in advance.
To substantiate the theoretical results, the authors carried out comparative numerical simulations using identical parameters and identical initial conditions for both control schemes. The simulation outcomes confirmed that both the state-feedback controller and the adaptive controller successfully synchronized the drive and response systems. Moreover, the comparative numerical tests demonstrated that the adaptive controller achieved essentially the same fast convergence rate as the state-feedback control scheme. The provided numerical simulation examples illustrate the overall effectiveness and practical applicability of the obtained theoretical criteria, successfully addressing a notable gap in the existing literature regarding delayed fractional-order complex-valued memristive systems.
Subject of Research: Mittag-Leffler synchronization of delayed complex-valued fractional-order memristor-based neural networks
Article Title: Mittag-Leffler Synchronization of Leakage and Time-Varying Delayed Complex-Valued Fractional-Order Memristor-Based Neural Networks
Article References: Ma, S., & Zhang, N. (2026). Mittag-Leffler Synchronization of Leakage and Time-Varying Delayed Complex-Valued Fractional-Order Memristor-Based Neural Networks. Neural Processing Letters. https://doi.org/10.1007/s11063-026-11895-6
Image Credits: AI Generated
DOI: 10.1007/s11063-026-11895-6
Keywords: neural networks, memristors, Mittag-Leffler synchronization, fractional-order systems, complex-valued neural networks, time-varying delays, leakage delays, adaptive control, Mittag-Leffler, Synchronization, Leakage, Time-Varying
News Source: Denise Maddox. (November 7, 2026). Global Mittag-Leffler Synchronization Established for Delayed Complex-Valued Memristive Networks. Scienmag.
