Extensive research has demonstrated that memristors or trigonometric functions can enhance the complexity of discrete chaotic maps. This article introduces a four-dimensional trigonometric-based memristor hyperchaotic map (4D-TBMHM). By combining discrete memristors, sine, and cosine, the 4D-TBMHM exhibits complex dynamical behaviors. Bifurcation and multistability phenomena are demonstrated using numerical methods. The 4D-TBMHM demonstrates symmetric or attractor self-growth based on iteration length for various system control parameters and initial states, and its complicated complex fractal structure and exemplary performance metrics are also highlighted. Furthermore, an attractor hybrid control, capable of arbitrary positioning and shaping, is proposed. An field-programmable gate array (FPGA)-based hardware prototype is developed, and the attractors are experimentally captured. Moreover, by combining 4D-TBMHM with an arrayed linear feedback shift register, an ultra-fast pseudorandom number generator (UFPRNG) with a throughput of 195.2 Gbps is achieved on an FPGA, surpassing contemporary techniques. Last, the generated UFPRNG is employed for 2.8 Gbps signal generation with noise, and experimental results illustrate its remarkable real-time capability and the PRNG's inherent randomness, facilitating signal generation with any signal-to-noise ratios.

In the fault diagnosis field, the fault feature signal is weak and contaminated by the noise. The lock-in amplifier is a useful tool for weak signal detection. Aiming to the amplitude error of the lock-in amplifier caused by frequency deviation between the measured signal and the reference signal, a DFT-based automatic signal frequency estimation method is studied to improve the frequency accuracy of the reference signal. Based on this frequency estimation method, a software digital lock-in amplifier method is proposed to detect the multiple frequencies signals. This proposed method can automatically measure the frequency value of the measured signal without prior frequency information. Then, the reference signals are generated through this frequency value to make the digital lock-in amplifier estimate the amplitude of the measured signal. Moreover, an iterative structure is used to implement the multiple frequencies signal measurement. The frequencies and amplitudes measurement accuracies are tested. Under different SNR conditions, the frequency relative error is less than $0.1\%$. In addition, the amplitude relative error with different signal frequencies is less than $1.7\%$ when the SNR is −1 dB. This proposed software digital lock-in amplifier method has a higher signal frequency tracking ability and amplitude measurement accuracy.

A single silicon island concave silicon micro-resonant pressure sensor based on frequency difference is proposed in this paper. The resonator is designed for electrostatic drive and electrostatic detection, and the lateral synovial motion is taken as the working mode, so that the structure has the characteristics of structural stability and small coupling, and the force mode is torque transmission. The structure was simulated by finite element analysis, and the structure size was determined. The working range of the overall structure was 0~300kPa, and the simulation verified that the working mode order in the range did not change with the increase of pressure, ensuring the linearity of the output. The operating resonant frequencies of the resonator are 53,324.15Hz and 54,721.82Hz. The effect of the small deflection deformation of the sensitive film and the inclination Angle of the silicon island on the sensitivity of the resonator is analyzed by simulation, and the location of the silicon island is determined. The feasibility of resonator structure is confirmed by frequency domain response analysis, and the sensitivity of resonator can reach 50.48Hz/kPa.

The frequency of a weak signal is used for fault diagnosis and target identification in various fields. By introducing particle swarm optimization (PSO) and spectral entropy (SE), an automated weak signal frequency estimation method based on the Duffing oscillator is proposed. The proposed method uses the differential structure to enhance the timing difference of the Duffing oscillator between the chaotic and large-scale periodic states, which is quantitatively distinguished by SE. Then, the frequency of the internal driving force is adaptively adjusted by the PSO to allow the SE to reach a minimum value where the driving frequency equals the weak signal frequency. A group of weak signals with different frequencies has been tested. The maximum relative frequency error is only 0.68%. Unlike other chaotic oscillator-based frequency estimation methods, the proposed method does not need to determine the phase state manually. A rough initial frequency search range is sufficient for automatic frequency measurement of the proposed method in this paper.

The integration of modern accelerometers and gyroscopes has led to the development of inertial measurement units (IMUs), which have evolved into inertial navigation systems (INS) and, more recently, into positioning, navigation, and timing (PNT) systems. Furthermore, multi-sensor on-chip technology is advancing, delivering wider bandwidths, heightened precision, and further miniaturization. Optomechanical sensor research reveals significant advantages over conventional accelerometers, particularly in the achievement of low-noise resonant optomechanical transduction, which approaches the thermodynamic limit. In this study, we further present a differential-type optomechanical accelerometer based on the two-dimensional slot-type silicon photonic crystal (PhC) micro-cavity from the low-frequency region to near the fundamental resonance frequency. It is demonstrated that, in the parametric optomechanical oscillation mode, the silicon-on-insulator (SOI) sensor has a measured noise-equivalent acceleration (NEA) of ~20 μg/Hz ^1/2 , nearing the thermal noise limit of ~14 μg/Hz ^1/2 . The sensor, designed for broadband vibration measurements, is engineered with a theoretical bandwidth of ~70 kHz, but can only be measured up to 30 kHz due to instrumentation limitations. This device is suitable for various applications such as vibration detection, inertial navigation, acoustic analysis, or optical sensing collaboration.

This study introduces a two-dimensional sine-based hyperchaotic map (2D-SBHM), which leverages the boundedness and periodicity of sinusoidal functions to enhance chaotic performance. The 2D-SBHM exhibits multiple fixed points, with variations in system parameters (SPs) inducing diverse bifurcation behaviors. Numerical analysis reveals a maximal chaotic range of [-40, 40] and a high permutation entropy of 6.433, outperforming several existing 2D sine-based maps in stochastic metrics. The coexistence of attractors, including heterogeneous and homogeneous types derived from SPs, is explored. Four cases of homogeneous attractors generated from initial states are presented. A modular arithmetic method is proposed for generating homogeneous attractors, allowing the creation of attractor sets in quantities such as 3, 5, 15, 20, or 30. Furthermore, a high-precision hardware implementation strategy using FPGA and DAC architectures is developed, enabling theoretical calculations for oscilloscope amplitude scaling and display area. An FPGA-based hardware platform is constructed to verify the proposed approach and realize a pseudo-random number generator with a throughput rate of 2.8 Gbps. To the best of our knowledge, this work represents the first demonstration of arbitrary homogeneous attractor generation in a discrete chaotic map using modular arithmetic, coupled with the first high-precision hardware implementation of chaotic attractors.