Synchronization Dynamics in Inertial Neural Networks
Summary
Inertial neural networks incorporate second-order dynamics that account for momentum or “inertia” in the evolution of neuronal states. Such models capture richer temporal behaviours than their first-order counterparts, including oscillations, convergence delays and transient memory effects. Synchronization dynamics in these networks describe the process by which coupled units evolve towards identical or phase-locked trajectories under the influence of delayed interactions and feedback controls. The study of synchronization in inertial architectures has attracted growing interest owing to its implications for neuromorphic computing, secure communications and coordinated control in robotic swarms. Analytical approaches typically employ Lyapunov-based functionals and matrix measures to derive delay-dependent criteria for global exponential, asymptotic or finite-time synchronisation. Recent advances have extended these methods to fractional-order dynamics and memristor-based couplings, yielding more flexible frameworks for fast convergence and stability under variable time delays. Computational experiments validate theoretical bounds and demonstrate potential applications in pattern recognition, chaos control and energy-efficient signal processing.
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Synchronization Dynamics in Inertial Neural Networks publication trend
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Technical terms
Inertial neural network: A network model characterised by second-order differential equations that include a momentum term, capturing transient dynamics and overshoot phenomena.
Synchronization: The process by which interconnected systems adjust their states to exhibit identical trajectories or a fixed phase relationship over time.
Finite-time stability: A property whereby a system’s state converges to a desired equilibrium within a finite time interval, rather than asymptotically.
Fractional-order dynamics: A generalisation of classical dynamics where derivatives of non-integer order impart extended memory effects to system evolution.
Memristor: A resistive device whose conductance depends on the history of voltage or current, used to implement adaptive synaptic weights in neural architectures.
References
- Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach. Neural Networks (2020).
- New Results on Finite-Time Synchronization Control of Chaotic Memristor-Based Inertial Neural Networks with Time-Varying Delays. Mathematics (2023).
- Asymptotic and Finite-Time Synchronization of Fractional-Order Memristor-Based Inertial Neural Networks with Time-Varying Delay. Fractal and Fractional (2022).
- Exponential Synchronization in Inertial Neural Networks with Time Delays. Electronics (2019).
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