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Since the unsaturating activation function is unbounded, more complex dynamics may exist in neural networks with this kind of activation function. In this article, monostability and multistability results of almost-periodic solutions are developed for fractional-order neural networks with unsaturating piecewise linear activation functions. Some globally Mittag-Leffler attractive sets are given, and the existence of globally Mittag-Leffler stable almost-periodic solution is demonstrated by using Ascoli–Arzela theorem. In particular, some sufficient conditions are provided to ascertain the multistability of almost-periodic solutions based on locally positively invariant set. It shows that there exists an almost-periodic solution in each positively invariant set, and all trajectories converge to this periodic trajectory in that rectangular area. Two illustrative examples are provided to demonstrate the effectiveness of the proposed sufficient criteria. [ABSTRACT FROM AUTHOR]

Electronic reconnaissance technology has received increased attention in aerospace applications owing to its ability to analyze signals from space radiation sources. As the routine signal of satellites, the Unified S-Band (USB) Telemetry Tracking and Command (TT&C) waveform has become a crucial target of electronic reconnaissance. The modulation index of the USB TT&C waveform is a critical factor that affects the spectral characteristics of the waveform and quality of TT&C services. This parameter can be regarded as a critical feature for identifying non-cooperative targets. Considering the estimation of this parameter is an imminent requirement, a non data-aided method of modulation index is proposed. The algorithmic framework of the proposed method is based on Fourier transform and spectral analysis. The theoretical root mean squared error of the method is derived in detail, and the factors affecting the accuracy of the method are discussed. The accuracy of the method is assessed via the Monte Carlo simulation and the robustness of the method is verified using actual signals. The experimental results reveal that the accuracy of the method can reach 10−2 in a real-life electromagnetic environment where the signal-to-noise ratio is approximately −8 dB. • Modulation index estimation for USB TT&C waveform with sinusoidal tone. • Proposed estimator overcome the uselessness of existing methods for our target. • Verification of the validity and robustness of the estimator by actual signals. • Easy to implement in engineering applications. [ABSTRACT FROM AUTHOR]