Finally, the proposed ASMC approaches are assessed and validated through the execution of numerical simulations.
Employing nonlinear dynamical systems, researchers study brain functions and the impact of external disruptions on neural activity across a multitude of scales. To investigate efficient, stimulating control signals aligning neural activity with desired targets, we delve into optimal control theory (OCT) methods. Efficiency is measured by a cost function, which considers the trade-off between control strength and closeness to the desired activity. Pontryagin's principle allows for the derivation of the cost-minimizing control signal. An OCT analysis was conducted on a Wilson-Cowan model featuring coupled excitatory and inhibitory neural populations. A characteristic oscillatory behavior is observed in the model, alongside fixed points representing low and high activity states, and a bistable region where both low and high activity states coexist simultaneously. see more A method for finding an optimal control is applied to a state-switching (bistable) system and a phase-shifting (oscillatory) one, which permits a limited transition time before punishing deviations from the target state. Limited-strength input pulses are used for the state-switching operation, subtly guiding the activity to the target's basin of attraction. see more The transition period's length does not induce qualitative changes to the pulse shapes. The full transition period of the phase-shifting operation is characterized by the presence of periodic control signals. Decreasing amplitudes accompany longer transition intervals, and the shapes of these responses are linked to the model's sensitivity to phase shifts induced by pulsed perturbations. Control strength, penalized by the integrated 1-norm, generates control inputs exclusively aimed at a single population across both tasks. Depending on the position within the state space, control inputs either activate the excitatory or inhibitory population.
The recurrent neural network paradigm known as reservoir computing, where only the output layer is trained, has demonstrated its remarkable ability in tasks such as nonlinear system prediction and control. It has recently been shown that adding time-shifts to signals originating from a reservoir results in considerable improvements in performance accuracy. Our work introduces a method to choose time-shifts that maximize the rank of the reservoir matrix, utilizing a rank-revealing QR algorithm. This technique, unbound by task requirements, does not rely on a system model, rendering it directly applicable to analog hardware reservoir computers. Our time-shift selection approach is demonstrated on two distinct reservoir computer types: one being an optoelectronic reservoir computer, and the other a conventional recurrent network utilizing a hyperbolic tangent 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 circle map's ability to model the dynamics of the original nonlinear system of ordinary differential equations is proven. This model also allows the identification of conditions for resonant synchronization, resulting in output frequency combs with tunable shape characteristics. The potential for substantial photonic signal-processing applications is present in these theoretical developments.
Within a viscous and noisy environment, this report focuses on a collection of interacting self-propelled particles. The analysis of the explored particle interaction indicates no ability to discern between the alignment and anti-alignment characteristics of self-propulsion forces. In particular, we examined a collection of self-propelled, non-polar, attractively aligned particles. As a result, the absence of a global velocity polarization within the system prevents a genuine flocking transition. Rather, the system exhibits self-organized motion, featuring the formation of two flocks moving in opposing directions. The short-range interaction is a consequence of this tendency, triggering the generation of two counter-propagating clusters. Parameters dictate how these clusters interact, showcasing two of the four fundamental counter-propagating dissipative soliton behaviors, without implying that any single cluster qualifies as a soliton. Their movement continues after the clusters interpenetrate or bond, remaining together. Two mean-field strategies are applied to analyze this phenomenon. The first, an all-to-all interaction, predicts the formation of two counter-propagating flocks. The second, a noiseless approximation for cluster-to-cluster interactions, accounts for the solitonic-like behaviors. Furthermore, the ultimate approach indicates that the bound states are in a metastable state. Direct numerical simulations of the active-particle ensemble align with both approaches.
Within a time-delayed vegetation-water ecosystem impacted by Levy noise, the stochastic stability of the irregular attraction basin is investigated. Our initial discussion centers on the invariance of deterministic model attractors to changes in average delay time, contrasting this with the consequential impact on their respective attraction basins, culminating in a presentation of Levy noise generation. Next, we examine the ecosystem's sensitivity to probabilistic parameters and delay times by analyzing the first escape probability (FEP) and the mean first exit time (MFET). The numerical algorithm for determining FEP and MFET values within the irregular attraction basin is demonstrably accurate through the use of Monte Carlo simulations. Lastly, the FEP and MFET contribute to the definition of the metastable basin, demonstrating the consistency of the two indicators' results. The stochastic stability parameter, particularly the noise intensity, is demonstrated to diminish the basin stability of vegetation biomass. Time delays in this environment reliably reduce the instability exhibited by the system.
Propagating precipitation waves display a remarkable spatiotemporal dynamic, arising from the combined influence of reaction, diffusion, and precipitation. We are analyzing a system comprising 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. Complex spatiotemporal waves, including counter-rotating spiral waves, target patterns, and the annihilation of waves upon collision, are observed within the propagating precipitation band. Experiments on thin gel sections have demonstrated the propagation of diagonal precipitation patterns within the main precipitation zone. Two horizontally propagating waves demonstrate a merging pattern, resulting in a single wave, as observed in these waves. see more Developing a detailed understanding of complex dynamical behavior is achievable through the use of computational modeling.
Open-loop control is a demonstrated effective approach for controlling thermoacoustic instability, which presents as self-excited periodic oscillations, in turbulent combustors. We report experimental findings and a synchronization model for thermoacoustic instability suppression, using a rotating swirler within a lab-scale turbulent combustor. 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 enhance the Dutta et al. [Phys. model to capture the transition and quantify its synchronization aspects. The acoustic system in Rev. E 99, 032215 (2019) is coupled with a feedback loop from the phase oscillator ensemble. Evaluating the effects of acoustic and swirl frequencies allows for the determination of the coupling strength in the model. An optimization algorithm is implemented to establish a concrete quantitative connection between the theoretical model and the empirical results. 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. Significantly, our examination of flame dynamics reveals that the model, independent of spatial information, accurately reproduces the spatiotemporal synchronization of local heat release rate fluctuations and acoustic pressure, which is crucial for transitioning to the suppression state. In consequence, the model emerges as a powerful tool for elucidating and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where intricate spatial and temporal interactions produce diverse dynamic events.
This paper introduces an observer-based, event-triggered, adaptive fuzzy backstepping synchronization control for uncertain fractional-order chaotic systems, addressing disturbances and partially unmeasurable states. Unknown functions in backstepping are estimated using fuzzy logic systems. To avert the explosive escalation of complexity in the problem, a fractional-order command filter was specifically engineered. To mitigate filter error and enhance synchronization precision, a sophisticated error compensation mechanism is concurrently implemented. A disturbance observer is formulated for circumstances of unmeasurable states, and a supplementary state observer is developed to ascertain the synchronization error of the master-slave system.