Verification of the effectiveness of the proposed ASMC approaches is performed via numerical simulations.

Nonlinear dynamical systems, exploring neural activity at various scales, are frequently used to analyze brain functions and the consequences of outside disruptions. We analyze optimal control theory (OCT) to develop control strategies for producing stimulating signals, ensuring neural activity consistently aligns with desired targets. The cost functional, a measure of efficiency, evaluates the trade-off between control strength and proximity to the target activity. Using Pontryagin's principle, the control signal minimizing the cost can be calculated. The Wilson-Cowan model, featuring coupled excitatory and inhibitory neural populations, was then subjected to OCT analysis. The model's behavior includes oscillations, stable low- and high-activity states, and a bistable region where coexisting low and high activity levels are observed. Lithocholic acid We determine an optimal control strategy for a state-switching (bistable) system and a phase-shifting (oscillatory) task, allowing for a finite transition period before penalizing deviations from the target state. For state transitions, input pulses of restricted force subtly shift activity into the attractor basin. Lithocholic acid The qualitative characteristics of pulse shapes remain constant regardless of the transition duration. Periodic control signals are used to affect the phase-shifting over the entire transition phase. Amplitudes shrink in response to extended transition phases, while their characteristics are linked to the model's sensitivity to pulsed phase shifts. The integrated 1-norm penalization of control strength results in control inputs focused on a single population for both tasks. The excitatory or inhibitory population's response to control inputs is contingent upon the current state-space location.

A recurrent neural network paradigm, reservoir computing, where only the output layer is trained, has shown exceptional ability in tasks such as nonlinear system prediction and control. Reservoir-generated signals, when augmented with time-shifts, have recently been shown to dramatically improve performance accuracy. This paper describes a technique to determine time-shifts by maximizing the reservoir matrix's rank via a rank-revealing QR algorithm. This technique, unconstrained by any task, does not necessitate a model of the system; consequently, it is directly applicable to analog hardware reservoir computers. Our time-shifted selection technique is showcased using two reservoir computer models: an optoelectronic reservoir computer and a traditional recurrent network with hyperbolic tangent activation as the activation function. Our technique yields significantly enhanced accuracy, surpassing random time-shift selection in practically all cases.

Under the influence of an injected frequency comb, the response of a tunable photonic oscillator, composed of an optically injected semiconductor laser, is examined, leveraging the time crystal concept, a well-established tool for analyzing driven nonlinear oscillators in mathematical biology. A one-dimensional circle map encapsulates the dynamics of the initial system, its properties and bifurcations uniquely determined by the time crystal's specific details and fully explicating the limit cycle oscillation's phase response. The dynamics of the original nonlinear system of ordinary differential equations are precisely captured by the circle map, which can also predict conditions conducive to resonant synchronization, leading to output frequency combs with adjustable shape characteristics. The potential for substantial photonic signal-processing applications is present in these theoretical developments.

Interacting self-propelled particles are considered in this report, embedded within a viscous and noisy environment. Examination of the particle interaction under study shows that the alignment and anti-alignment of the self-propulsion forces are not distinguished. Specifically, our study encompassed a set of self-propelled, apolar, and attractively aligning particles. Predictably, the system's global velocity polarization is absent, leading to no authentic flocking transition. Instead, a self-organizing movement ensues, with the system manifesting two flocks traveling in contrary directions. This inclination results in the development of two clusters propagating in opposite directions for short-range interactions. These clusters interact in accordance with the parameters, exhibiting two of the four defining counter-propagating dissipative soliton behaviors, but with no cluster having to be specifically recognized as a soliton. Despite colliding or forming a bound state, the clusters' movement continues, interpenetrating while remaining united. This phenomenon is analyzed by applying two mean-field strategies. An all-to-all interaction strategy predicts the emergence of two counter-propagating flocks, while a noiseless approximation for the cluster-to-cluster interaction explains the phenomenon's solitonic-like characteristics. In addition, the last procedure suggests that the bound states are of a metastable nature. The active-particle ensemble's direct numerical simulations concur with both approaches.

An investigation into the stochastic stability of the irregular attraction basin within a time-delayed vegetation-water ecosystem, subject to Levy noise, is undertaken. We begin by analyzing the unchanged attractors of the deterministic model despite variations in average delay time, and the subsequent modifications to their corresponding attraction basins. This is followed by the introduction of Levy noise generation. Our subsequent analysis focuses on the effect of random parameters and latency periods on the ecosystem, measured by the first escape probability (FEP) and the mean first exit time (MFET). Monte Carlo simulations effectively verify the implemented numerical algorithm for calculating FEP and MFET within the irregular attraction basin. Furthermore, the metastable basin's boundaries are dictated by the FEP and the MFET, thereby reinforcing the concordance of the results reflected by both indicators. The basin stability of the vegetation biomass is adversely affected by the stochastic stability parameter, especially its noise intensity. Under these circumstances, the time delay phenomenon effectively compensates for any instability.

Spatiotemporal patterns of precipitation waves, a remarkable phenomenon, emerge from the intricate interplay of reaction, diffusion, and precipitation. The system we are studying incorporates a sodium hydroxide outer electrolyte and an aluminum hydroxide inner electrolyte. A redissolution Liesegang system exhibits a descending precipitation band that progresses through the gel, marked by precipitate formation at its front and dissolution at its rear. Counter-rotating spiral waves, target patterns, and the annihilation of colliding waves are components of the complex spatiotemporal waves occurring within propagating precipitation bands. Our investigations, including experiments on thin gel slices, have uncovered propagating diagonal precipitation waves within the principal precipitation band. These waves showcase a wave-merging effect, where two horizontally propagating waves unify into a single wave form. Lithocholic acid Computational modeling provides a means to gain a profound understanding of intricate dynamical behaviors.

Turbulent combustors experiencing thermoacoustic instability, a form of self-excited periodic oscillation, find open-loop control to be an effective method. In this study, we present experimental data and a synchronization model for the suppression of thermoacoustic instability in a lab-scale turbulent combustor, which involves rotating the swirler. Within the context of combustor thermoacoustic instability, a progressive increase in swirler rotation speed results in a transition from limit cycle oscillations to low-amplitude aperiodic oscillations, with an intermediary period of intermittency. We develop an improved framework based on the Dutta et al. [Phys. model to characterize the transition and quantify the underlying synchronization. Rev. E 99, 032215 (2019) utilizes a feedback loop linking the phase oscillator ensemble to the acoustic component. By taking into account the influences of acoustic and swirl frequencies, the model's coupling strength is determined. Quantitative validation of the model against experimental data is achieved through the application of an optimization algorithm for parameter estimation. We verify the model's capability to reproduce the bifurcations, the nonlinear dynamics in time series data, the probability density function profiles, and the amplitude spectrum of acoustic pressure and heat release rate fluctuations occurring in the various dynamical states as the system transitions to suppression. Undeniably, our analysis emphasizes flame dynamics, showcasing that a model without any spatial input effectively mirrors the spatiotemporal synchronicity of fluctuations in local heat release rate and acoustic pressure, fundamentally linked to the suppression state. Therefore, the model proves a formidable instrument for explaining and directing instabilities in thermoacoustic and other expansive fluid dynamical systems, wherein spatial and temporal interplays generate complex dynamic phenomena.

An event-triggered, adaptive fuzzy backstepping synchronization control, based on an observer, is developed in this paper to address the problem of uncertain fractional-order chaotic systems with disturbances and partially unmeasurable states. To evaluate unknown functions within the backstepping procedure, fuzzy logic systems are employed. A fractional-order command filter is devised to circumvent the escalating complexities of the problem. To enhance both synchronization accuracy and reduce filter errors, a novel error compensation mechanism is simultaneously implemented. For instances involving unmeasurable states, a disturbance observer is developed; subsequently, a state observer is established to estimate the synchronization error inherent in the master-slave system.