Cavity optomechanics provides a powerful platform for observing many interesting classical and quantum nonlinear phenomena due to the radiation-pressure coupling between its optical and mechanical modes. In particular, the chaos induced by optomechanical nonlinearity has been of great concern because of its importance both in fundamental physics and potential applications ranging from secret information processing to optical communications. This review focuses on the chaotic dynamics in optomechanical systems. The basic theory of general nonlinear dynamics and the fundamental properties of chaos are introduced. Several nonlinear dynamical effects in optomechanical systems are demonstrated. Moreover, recent remarkable theoretical and experimental efforts in manipulating optomechanical chaotic motions are addressed. Future perspectives of chaos in hybrid systems are also discussed.

OBJECTIVE: It is known that long-term stress leads to trauma and very often to depression. Usually, the diagnosis of depression is dealt with by psychiatrists who, based on conversations and questions, diagnose the patient\'s illness and condition. Unfortunately, this diagnosis is not always reliable. To prevent the development of disease, it is necessary to detect illness in a timely manner. One of the indications of the possibility of the onset of disease is a disturbance in the level of hormones in the body, especially cortisol. The purpose of this study was to develop a mathematical model for cortisol variation resulting from stress which would be useful in making conclusions about depressive states.
METHODS: Rapid changes in cortisol concentration, according to ultradian rhythms, which are much faster than the daily circadian rhythm, is modelled as a truly nonlinear oscillator. The mathematical model contains two coupled first order differential equations. The stress is modeled as a pulsating action, described with a periodic trigonometric function, and cortisol production as a cubic nonlinear one. Three models for cortisol variation are considered: 1) the pure nonlinear model, 2) the periodically excited system, 3) and the chaotic system. The results from the study are supported with experimental measurements.
RESULTS: Without stress, cortisol variation is of an oscillatory type with a constant steady-state amplitude. Intensive stress causes a resonant phenomenon in cortisol oscillatory variation. The occasion is short and is usually without consequences. For long stress periods deterministic chaos occurs which permanently changes the levels of cortisol. This phenomenon is an indicator of depression. Results from the suggested models are compared with experimentally obtained ones and good quantitative agreement is obtained.
CONCLUSIONS: The nonlinear oscillator is a good model for indication of depression. The model provides not only general conclusions, but also individual ones, if personal characteristics are taken into consideration. Response of the model depends not only on the input data related to stress, but also on the system parameters that specify each individual. Findings obtained from this study have implications for the medical diagnosis and treatment of depression.

Memristors are of great theoretical and practical significance for chaotic dynamics research of brain-like neural networks due to their excellent physical properties such as brain synapse-like memorability and nonlinearity, especially crucial for the promotion of AI big models, cloud computing, and intelligent systems in the artificial intelligence field. In this paper, we introduce memristors as self-connecting synapses into a four-dimensional Hopfield neural network, constructing a central cyclic memristive neural network (CCMNN), and achieving its effective control. The model adopts a central loop topology and exhibits a variety of complex dynamic behaviors such as chaos, bifurcation, and homogeneous and heterogeneous coexisting attractors. The complex dynamic behaviors of the CCMNN are investigated in depth numerically by equilibrium point stability analysis as well as phase trajectory maps, bifurcation maps, time-domain maps, and LEs. It is found that with the variation of the internal parameters of the memristor, asymmetric heterogeneous attractor coexistence phenomena appear under different initial conditions, including the multi-stable coexistence behaviors of periodic-periodic, periodic-stable point, periodic-chaotic, and stable point-chaotic. In addition, by adjusting the structural parameters, a wide range of amplitude control can be realized without changing the chaotic state of the system. Finally, based on the CCMNN model, an adaptive synchronization controller is designed to achieve finite-time synchronization control, and its application prospect in simple secure communication is discussed. A microcontroller-based hardware circuit and NIST test are conducted to verify the correctness of the numerical results and theoretical analysis.

Spiking neural networks (SNNs) have superior energy efficiency due to their spiking signal transmission, which mimics biological nervous systems, but they are difficult to train effectively. Although surrogate gradient-based methods offer a workable solution, trained SNNs frequently fall into local minima because they are still primarily based on gradient dynamics. Inspired by the chaotic dynamics in animal brain learning, we propose a chaotic spiking backpropagation (CSBP) method that introduces a loss function to generate brain-like chaotic dynamics and further takes advantage of the ergodic and pseudo-random nature to make SNN learning effective and robust. From a computational viewpoint, we found that CSBP significantly outperforms current state-of-the-art methods on both neuromorphic data sets (e.g. DVS-CIFAR10 and DVS-Gesture) and large-scale static data sets (e.g. CIFAR100 and ImageNet) in terms of accuracy and robustness. From a theoretical viewpoint, we show that the learning process of CSBP is initially chaotic, then subject to various bifurcations and eventually converges to gradient dynamics, consistently with the observation of animal brain activity. Our work provides a superior core tool for direct SNN training and offers new insights into understanding the learning process of a biological brain.

In this paper, we present a fully integrated circuit without inductance implementing Chua\'s chaotic system. The circuit described in this study utilizes the SMIC 180 nm CMOS process and incorporates a multi-path voltage-controlled oscillator (VCO). The integral-differential nonlinear resistance is utilized as a variable impedance component in the circuit, constructed using discrete devices from a microelectronics standpoint. Meanwhile, the utilization of a multi-path voltage-controlled oscillator ensures the provision of an adequate oscillation frequency and a stable waveform for the chaotic circuit. The analysis focuses on the intricate and dynamic behaviors exhibited by the chaotic microelectronic circuit. The experimental findings indicate that the oscillation frequency of the VCO can be adjusted within a range of 198 MHz to 320 MHz by manipulating the applied voltage from 0 V to 1.8 V. The circuit operates within a 1.8 V environment, and exhibits power consumption, gain-bandwidth product (GBW), area, and Lyapunov exponent values of 1.0782 mW, 4.43 GHz, 0.0165 mm2, and 0.6435∼1.0012, respectively. The aforementioned circuit design demonstrates the ability to generate chaotic behavior while also possessing the benefits of low power consumption, high frequency, and a compact size.

The insect predator-prey system mediates several feedback mechanisms which regulate species abundance and spatial distribution. However, the spatiotemporal dynamics of such discrete systems with the refuge effect remain elusive. In this study, we analyzed a discrete Holling type II model incorporating the refuge effect using theoretical calculations and numerical simulations, and selected moths with high and low growth rates as two exemplifications. The result indicates that only the flip bifurcation opens the routes to chaos, and the system undergoes four spatiotemporally behavioral patterns (from the frozen random pattern to the defect chaotic diffusion pattern, then the competition intermittency pattern, and finally to the fully developed turbulence pattern). Furthermore, as the refuge effect increases, moths with relatively slower growth rates tend to maintain stability at relatively low densities, whereas moths with relatively faster growth rates can induce chaos and unpredictability on the population. According to the theoretical guidance of this study, the refuge effect can be adjusted to control pest populations effectively, which provides a new theoretical perspective and is a feasible tool for protecting crops.

The origin of fast radio bursts (FRBs), the brightest cosmic explosion in radio bands, remains unknown. We introduce here a novel method for a comprehensive analysis of active FRBs\' behaviors in the time-energy domain. Using \"Pincus Index\" and \"Maximum Lyapunov Exponent\", we were able to quantify the randomness and chaoticity, respectively, of the bursting events and put FRBs in the context of common transient physical phenomena, such as pulsar, earthquakes, and solar flares. In the bivariate time-energy domain, repeated FRB bursts\' behaviors deviate significantly (more random, less chaotic) from pulsars, earthquakes, and solar flares. The waiting times between FRB bursts and the corresponding energy changes exhibit no correlation and remain unpredictable, suggesting that the emission of FRBs does not exhibit the time and energy clustering observed in seismic events. The pronounced stochasticity may arise from a singular source with high entropy or the combination of diverse emission mechanisms/sites. Consequently, our methodology serves as a pragmatic tool for illustrating the congruities and distinctions among diverse physical processes.

Physiological networks, as observed in the human organism, involve multi-component systems with feedback loops that contribute to self-regulation. Physiological phenomena accompanied by time-delay effects may lead to oscillatory and even chaotic dynamics in their behaviors. Analogous dynamics are found in semiconductor lasers subjected to delayed optical feedback, where the dynamics typically include a time-delay signature. In many applications of semiconductor lasers, the suppression of the time-delay signature is essential, and hence several approaches have been adopted for that purpose. In this paper, experimental results are presented wherein photonic filters utilized in order to suppress time-delay signatures in semiconductor lasers subjected to delayed optical feedback effects. Two types of semiconductor lasers are used: discrete-mode semiconductor lasers and vertical-cavity surface-emitting lasers (VCSELs). It is shown that with the use of photonic filters, a complete suppression of the time-delay signature may be affected in discrete-mode semiconductor lasers, but a remnant of the signature persists in VCSELs. These results contribute to the broader understanding of time-delay effects in complex systems. The exploration of photonic filters as a means to suppress time-delay signatures opens avenues for potential applications in diverse fields, extending the interdisciplinary nature of this study.

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.

The classical mathematical modeling of ultrasound acoustic bubble is so far using to improve the medical imaging quality. A clear and visible medical ultrasound image relies on bubble\'s diameter, wavelength and intensity of the scattered sound. A bubble with diameter much smaller than the sound wavelength is regarded as highly efficient source of sound scattering. The dynamical equation for a medical ultrasound bubble is primarily modeled in classical integer-order differential equation. Then a reduction of order technique is used to convert the modeled dynamic equation for the bubble surface into a system of incommensurate fractional-orders. The incommensurate fractional-order values are calculated directly, by using Riemann stability region. On the basis of stability the convergence and accuracy of the numerical scheme is also discussed in detail. It has been found that the system will remain stable and chaotic for the incommensurate values α1<0.737 and α2<2.80, respectively.