This study investigates the potential of advanced Machine Learning (ML) methodologies to predict fluctuations in the price of gold. The study employs data from leading global stock indices, the S&P500 VIX volatility index, major commodity futures, and 10-year bond yields from the US, Germany, France, and Japan. Lagged values of these features up to 10 previous days are also used. Four machine learning

A quasi-residual physics-informed neural network (QR_PINN) with efficient residual-like blocks, was investigated based on classical physics-informed neural network to solve nonlinear fractional Schrödinger equation and analyze the transmission of spatial optical solitons in saturable nonlinear media with fractional diffraction. A comprehensive verification of stable transmission of various solitons

We provide an effective numerical strategy for fractal-fractional pantograph differential equations (FFPDEs). The fractal-fractional derivative is considered in the Atangana–Riemann–Liouville sense. The scheme is based on fractional shifted Morgan-Voyce neural network (FShM-VNN). We introduce a new class of functions called fractional-order shifted Morgan-Voyce and some useful properties of these functions

This paper aims to investigate the predefined-time synchronization analysis for two different multiple-input-multiple-output systems. Firstly, based on the definition of predefined-time synchronization, we propose a novel Lyapunov function and a novel fast terminal sliding mode, each having corresponding sufficient conditions for predefined-time synchronization. Second, we respectively derive the novel

Considering the effect of the proportional delay, this paper deals with a class of octonion-valued recurrent neural networks with proportional delay. We do not need to decompose the octonion-valued recurrent neural networks into real-valued neural networks because the multiplication of octonion algebras does not satisfy the associativity and commutativity. We obtain several sufficient conditions for

Emergencies are usually accompanied by rumors, which are intertwined with each other and cause interactive effects, leading to crisis escalation and “secondary disasters”. How to control and weaken such an effect is a very important topic in the field of spread dynamics. In this paper, we consider the interaction between rumors and derivative rumors, introduce the IC control strategy, construct the

Network science has become an emerging and promising discipline within academia, which has induced extensive concern from a diverse range of realms including economics, social and computer science, mathematics and statistical mechanics. In this work, we investigate the impact of network topology on an N-player trust game by considering the second-order reputation rule. The model consists of three types

The emergence and mechanism of cooperation in social dilemmas have always been fundamental issues in evolutionary game theory. In this paper, we study the snowdrift game, in which individuals in a stronger position can gain additional benefits in cooperation with weaker individuals due to differences in status. Meanwhile, innocuous-type strong individuals will not harm their partners’ interests, while

The paper explores the event-triggered impulsive control for consensus problems in multi-agent systems (MASs) with actuation delay. Two types of event-triggered delayed impulsive control (ETDIC) schemes, predicated on continuous and periodic sampling, are proposed respectively. Several exponential consensus criteria for MASs are derived by using Lyapunov method. A correlation function is established

Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been widely applied in diverse disciplines, including thermodynamics, continuum mechanics, mathematical analysis, machine learning, etc. In this paper, we propose a new method for solving the inverse XDE (ODE, PDE, SDE) problems by utilizing the entropy balance equation instead of the original differential equations. This distinguishing

The general rogue wave solutions of long-wave–short-wave model are obtained by using the Kadomtsev–Petviashvili (KP) hierarchy reduction method. Unlike previous studies, we have refined the differential operators involved in the solutions by eliminating the recursiveness. Based on the simplified expression, the rogue wave patterns from the second to fifth order are displayed. Specifically, there are

In this paper, a novel fuzzy event-triggered control approach with guaranteed performance of practical finite-time tracking convergence is constructed for uncertain fractional-order nonlinear chaotic systems in the presence of time-varying input delay. Firstly, fuzzy logic systems are employed to deal with immeasurable systematic information. Secondly, fractional-order command filters are incorporated

Neuromorphic computing has the potential to overcome the limitations of the von Neumann Bottleneck and Moore's Law. Memristors, characterized by nanoscale, adjustable resistance, low power consumption, and non-volatility, are considered as one of the best candidates for neuromorphic computing. This paper utilizes an accurate model of VO2 locally active memristor fabricated by HRL Labs to construct

The Time-Fractional Schrödinger Equation (TFSE) is well-adjusted to study a quantum system interacting with its dissipative environment. The Quantum Speed Limit (QSL) time captures the shortest time required for a quantum system to evolve between two states, which is significant for evaluating the maximum speed in quantum processes. In this work, we solve exactly for a generic time-fractional single

This paper focuses on the stability and stabilization problems of continuous-time T-S fuzzy systems (TSFS) with variable delay. A new augmented Lyapunov–Krasovskii functional (LKF) is established by combining the negative quadratic term with the alterable delay-product-integral term. To further improve the results, an extended quadratic function negative-determination (QFND) lemma is proposed to deal

To study the gas transport characteristics in rough inorganic nanopores, the effective pore size models of circular and rectangular nanopores are established, considering the influence of the adsorption water film, rock surface roughness, effective stress and the shape of the nanopore section. On this basis, the gas flow patterns are coupled, and the gas transport models in circular and rectangular

The signal detection ability of nervous system is highly associated with nonlinear and collective behaviors in neuronal medium. Neuronal noise, which occurs as natural endogenous fluctuations in brain activity, is the most salient factor influencing this ability. Experimental and theoretical research suggests that noise is beneficial, not detrimental, for regular functioning of nervous system. In this

Can a simple oscillator system, as in cellular automata, sustain complex nature upon discretization in time and space? The answer is by no means trivial as even the most simple, two-state, nearest neighbours cellular automata can lead to Universal Turing Machine (UTM) computing power. This study analyses a recently proposed model consisting of a ring of identical excitable Adler-type oscillators with

This article explores the exact solutions of the variable order fractional derivative of the stochastic Ginzburg–Landau equation (GLE) using the G′G2-expansion method with the assistance of Matlab R2021a software. The paper presents three key aspects that contribute to its novelty: (1) Our study introduces and examines the variable order fractional derivative of the stochastic Ginzburg–Landau equation

The Hindmarsh–Rose is one of the best-known models of computational neuroscience. Despite its popularity as a neuron model, we demonstrate that it is also a complete cardiac model. We employ a method based on bifurcations of the interspike interval to redraw its phase diagram and reveal a cardiac region. This diagram bears great resemblance to that of the map-based model for neurons and cardiac cells

In this manuscript, we describe fractional differential equations with neutral, integral boundary conditions and mixed delay using Atangana–Baleanu derivatives, which include the generalized Mittag-Leffler kernel. We determine the existence and uniqueness of results and analysis by fixed point method. Moreover, we explained the stability of the fractional differential equation in the frame of Ulam–Hyers

Higher-order interactions between coupled oscillators in neural networks exhibit a series of collective behavior phenomena, especially synchronization, some of which cannot occur in pairwise interactions. Thus far, there has been little researches on whether the higher-order interactions affect other collective behaviors besides synchronization, such as the entrainment ability of the suprachiasmatic

Mass extinction is a phenomenon in the history of life on Earth when a considerable number of species go extinct over a relatively short period of time. The magnitude of extinction varies between the events, the most well known are the “Big Five” when more than half of all species went extinct. There were many extinctions with a smaller magnitude too. It is widely believed that the common trigger leading

Any complex real-world system that changes over time can be represented as a network. We analyze these networks using network theory-based techniques to infer useful information from them. An important problem associated with complex systems is the link prediction problem. It aims to find the possibility of future or missing links in a network. Existing similarity-based link prediction methods consider

Managing cardiac disease and abnormal heart rate variability is a challenging problem with its psychological impact on lifesaving intervention. The research presents a novel machine learning approach to paradigm dynamic pacemaker design based on fractional order modified Van der Pol oscillator system implemented to generate rich non-sinusoidal signals for cardiac intervention and treatment. The physical

Purpose: This study aims to explore the intricate and concealed chaotic structures of meminductor systems and their applications in applied sciences by utilizing fractal fractional operators (FFOs). Methods: The dynamical analysis of a three-dimensional meminductor system with FFO in the Caputo sense is presented, and a unique solution for the system is obtained via a novel contraction in an orbitally

This paper investigates the global dynamics of a new 3-dimensional fractional-order (FO) system that presents just cross-product nonlinearities. Firstly, the FO forced Lorenz-84 system is introduced and the stability of its equilibrium points, as well as the chaos control for their stabilization, are addressed. Secondly, dynamical behavior is further analyzed and bifurcation diagrams, phase portraits

A study of data on the Zika outbreak in Brazil in 2015–2016 provides knowledge that Zika infection can trigger brain disorders such as Guillain–Barré Syndrome in adults and microcephaly in newborns. Zika infection is a vector-borne disease most commonly transmitted to humans through an infected Aedes mosquito bite, which is also the primary vector for dengue. Thus, many cases of these two diseases

The minimum cut (min-cut) problem has been extensively investigated, and the corresponding algorithms have been used in many related problems. The recently proposed acceleration strategy based on tree-cut mapping has been shown to be an effective alternative, with a slight loss in acceleration accuracy. However, the existing method requires a large number of ineffective traversal passes in the high-overhead

Gonorrhea is a disease that is spread by sexual contact, and it can potentially cause infections in the genital region, the rectum, and even the throat. Due to the shared history between infected individuals and their sexual partners, infected individuals will likely continue to have sexual relations with those same partners. As a result, this article aims to investigate how memory affects the transmission

We present a novel method, called Dispersion Entropy for Graph Signals, DEG, as a powerful tool for analysing the irregularity of signals defined on graphs. DEG generalizes the classical dispersion entropy concept for univariate time series, enabling its application in diverse domains such as image processing, time series analysis, and network analysis. Furthermore, DEG establishes a theoretical framework

In this paper, the MGIW-ARIMA model is proposed to predict the newly diagnosed cases of COVID-19. The MGIW model is used to predict the trend components, and the ARIMA model is used to predict the random components. Finally, the prediction results of trend components and random components are added together to get the estimation results. The data of COVID-19 in the United States is used to verify and

In the context of complex-valued rectangular b-metric spaces, the present study investigates the stability of complex-valued neural networks (CVNNs) with fractional order. Using the generalized contraction principle, we address the suitable condition for uniform stability of fractionally ordered CVNNs and establish the existence and uniqueness of the equilibrium point. Few numerical results are presented

In aquatic environments, zooplankton often exhibits life habit of vertical migration and the phytoplankton-zooplankton predator-prey systems in different water layers are therefore coupled together. To uncover the nonlinear mechanisms of pattern dynamics in such coupled plankton system, a spatiotemporal model is developed in this research with the consideration of plankton horizontal diffusion and

The evolution of vegetation system in arid and semi-arid grazing areas is a complex dynamical system which depends not only on the rainfall, but also grazing intensity. Currently, most of the research focuses on the influence of rainfall, but the effects of grazing have not been fully understood. Simultaneously, the intraspecific competition delay widely exists in vegetation system. In this project

In this paper, we examine a stochastic vegetation-water model, where the Black–Karasinski process is introduced to characterize the random fluctuations in vegetation evolution. It turns out that Black–Karasinski process is a both mathematically and biologically reasonable assumption by comparison with existing stochastic modeling approaches. First, it is theoretically proved that the solution of the

We develop a strategy to properly analyse the entropy in a classical system originally envisaged by Maxwell and extended it to quantum systems (molten liquid and water interacting with photons). We exploit the renormalized interaction to evaluate the entropy-change in these systems and have unequivocally identified the following two assumptions to be physically false. The false assumptions are related

In this paper, a sliding mode control problem with variable convergence speed for impulsive stochastic systems based on the cart-pendulum model is investigated. Firstly, the cart-pendulum is modeled as impulsive stochastic system and the interval-driven stability criterion for variable convergence rate is given according to the idea of pole configuration. Meanwhile, the corresponding sliding mode surface

A Duffing-Holmes system containing nonlinear damping is used to investigate some dynamical properties of the system under the combined action of constant excitation and simple harmonic excitation. The harmonic balance method is used to find the main vibration equation of the system and obtain the amplitude-frequency response relationship. In the analysis of the global characteristics of the system

We consider the paradigmatic Kuramoto oscillators coupled via an adaptive mean-field variable that breaks the rotational symmetry. The evolution equation for the mean-field variable is governed by the linear ordinary differential equation corresponding to a low-pass filter with a time-scale parameter, which attenuates the mean-field signal by filtering its high frequency components. We find distinct

Locally active memristor is considered as an ideal device for building neuron circuits. In this study, a novel current-controlled Chua Corsage Memristor (CCM), which supplements the existing CCM family, is proposed to explore its unknown neuromorphic dynamics. The non-volatility of the current-controlled CCM is verified by its power-off plot and the locally active domain is identified by its DC I-V

In this paper, the number and distributions of limit cycles bifurcating from a double homoclinic loop and a double heteroclinic loop of piecewise smooth systems with three zones are considered. By introducing a suitable Poincaré map near the double homoclinic loop, three criteria are derived to judge its inner and outer stability. Then through stability-changing method, bifurcation theorems of limit

Pure-quartic solitons (PQSs) balanced by the fourth-order dispersion (FOD) and nonlinearity in weakly birefringent optical fibers exhibit unique characteristics that differ from those of traditional solitons. Owing to the long oscillating tail of the PQS, soliton trapping can be easily promoted either between the sub pulses inside the molecule or along the two polarization axes of the birefringent

We consider vortex solitons in large-scale arrays composed of N elliptical waveguides placed on a ring, which can be fabricated using fs-laser writing technique in transparent nonlinear dielectrics. By introducing variable twist angles between longer axes of neighboring elliptical waveguides on a ring, we create circular arrays with adjustable discrete rotational symmetry ranging from CN to C1, when

Integral input-to-state stability (iISS) for delayed networks control systems (DNCS) is studied. Based on Kirchhoff’s matrix tree theorem in graph theory, a novel Lyapunov-Krasovaskii functional with integral terms is constructed via the Lyapunov function of each node control system in DNCS and its corresponding topological structure. According to Lyapunov method, some analysis and inequality skills

This paper investigates a fractional order SIR epidemic model with specific functional response and Holling type II treatment rate with fractional derivative in the Caputo sense. A thorough investigation of the existence, uniqueness, non-negativity and boundedness of the solutions has been performed in the beginning. Stability of the equilibria is analysed in the section next to it. Bifurcation analysis

Chaotic time series are often encountered in real-world applications, where modeling and understanding such time series present a significant challenge. Existing simulation-based methods for characterizing chaotic behavior may be sensitive to the respective model settings, while data-driven methods cannot adapt well to irregularities and aperiodicity in chaotic time series during the prediction stage

Since many years ago, it has been only a priori assumption that the diversity of ecological demography is largely influenced by the direct interactions of predator and prey species. But over the years, it has also been recognized that an indirect effect can also affect the system more strongly. The effect of fear on prey species is that it restricts physical activities and feeding times of prey thereby

In public goods games, rewards have been demonstrated as an effective mechanism for sustaining cooperation among individuals. Rewarding cooperators are willing to incur personal costs to incentivize cooperative behavior. However, pure cooperators become second-order free-riders because they are not willing to bear these additional costs. To address this issue and ensure the effectiveness of the reward

In this paper, we present a generalization of diffusion on fractal combs using fractal calculus. We introduce the concept of a fractal comb and its associated staircase function. To handle functions supported on these combs, we define derivatives and integrals using the staircase function. We then derive the Fokker–Planck equation for a fractal comb with dimension α, incorporating fractal time, and

This manuscript is concerned with the existence and trajectory controllability of impulsive stochastic magnetohydrodynamics equation governed by the Rosenblatt process. In this work, the study is made without imposing the compactness conditions in the generator S(τ) of an analytic semigroup. The noise terms rely on both velocity and magnetic fields. Initially, we reformulated the considered system

In this article, we consider a three species Lotka–Volterra food web reaction–diffusion model with cycle, in which the intensity of the rate of preying on species 1 by species 2, the rate of preying on species 2 by species 3 and the rate of preying on species 3 by species 1 are in general asymmetrical. By suitably choosing cross diffusion coefficients as the bifurcation parameter, a spatially inhomogeneous

The present research focuses on the study of how acoustic radiation modes behave in an elastic shell that has trifurcated junctions and structural variations. To express the vibration of a thin, flexible shell, the Donnell–Mushtari equations are utilized. These modes possess non-orthogonal characteristics and form a system that is linearly dependent. To analyze the scattering phenomenon in an elastic

Trust game is a common framework for studying trust behavior between unrelated individuals. Previous theoretical research has found that network structure or reputation can promote trust and cooperation, but these studies often assume that interactions between players are one-time and investors have no choice but to invest, which is inconsistent with reality. Here we introduce the conditional investment

We study the set of visible lattice points in multidimensional hypercubes. The problems we investigate mix together geometric, probabilistic and number theoretic themes. For example, we prove that almost all self-visible triangles with vertices in the lattice of points with integer coordinates in W=([0,N]∩Z)d are almost equilateral having all sides almost equal to dN/6, and the sine of the typical

This article considers the exponential mobile stabilization control of linear parabolic partial differential equation (PDE) systems. Firstly, a stabilization scheme based on static output feedback (SOF) control and mobile actuator/sensor guidance is proposed. Next, the operator theory is used to discuss the well-posedness of closed-loop PDE systems. Thus, the SOF control and mobile guidance design

Cooperation is the foundation of ecosystems and the human society, and the reinforcement learning provides crucial insight into the mechanism for its emergence. However, most previous work has mostly focused on the self-organization at the population level, the fundamental dynamics at the individual level remains unclear. Here, we investigate the evolution of cooperation in a two-agent system, where

In this article, the complex dynamics of susceptible-infected-treated-recovered (SITR) model describing the COVID-19 transmission is explored. Two types of transmission are included here, such as bi-linear with unaware susceptible individuals and nonlinear with aware susceptible individuals. Modified saturation recovery in treated individuals and a difference self-quarantined parameter in susceptible

The COVID-19 pandemic has been spreading all over the world, causing a serious blow to human beings. The hierarchical lockdown control measure, which is widely used, can effectively curb the spread of the virus. However, recent studies have shown that the lockdown measure may be the main culprit in increasing the injury rate of elite footballers. In fact, little is known about the effects of the lockdown

We propose an extension of the Fitzhugh-Nagumo model, which possesses a regime of three coexisting stable states: resting equilibrium and two stable oscillatory states. Such a regime is absent in the original Fitzhugh-Nagumo model but it is known to exist in higher-dimensional conductance based neuronal models. Thus, the proposed system provides a simpler two-dimensional model with such a property