Search Results (537)

The intelligent transformation of the wastewater treatment industry, as a core component of the modern environmental governance system, is of decisive significance for achieving sustainable development goals. This study focuses on the issue of multi-stakeholder collaborative governance in the intelligent transformation of the wastewater treatment industry, with differential game theory as the core framework. A tripartite game model involving the government, wastewater treatment enterprises, and digital twin platforms is developed to depict the dynamic interrelations and mutual influences of strategy choices, thereby capturing the coordination mechanisms among government regulation, enterprise technology adoption, and platform support in the transformation process. Based on the dynamic optimization properties of differential games, the Hamilton–Jacobi–Bellman (HJB) equation is employed to derive the long-term equilibrium strategies of the three parties, presenting the evolutionary paths under Nash non-cooperative games, Stackelberg games, and tripartite cooperative games. Furthermore, the Sobol global sensitivity analysis is applied to identify key parameters influencing system performance, while the response surface method (RSM) with central composite design (CCD) is used to quantify parameter interaction effects. The findings are as follows: (1) compared with Nash non-cooperative and Stackelberg games, the tripartite cooperative strategy based on the differential game model achieves global optimization of system performance, demonstrating the efficiency-enhancing effect of dynamic collaboration; (2) the most sensitive parameters are β, α, μ₃, and η₃, with β having the highest sensitivity index (STᵢ = 0.459), indicating its dominant role in system performance; (3) significant synergistic enhancement effects are observed among α–β, α–μ₃, and β–μ₃, corresponding, respectively, to the “technology stability–benefit conversion” gain effect, the “technology decay–platform compensation” dynamic balance mechanism, and the “benefit conversion–platform empowerment” performance threshold rule. Full article

One among the most intriguing results coming from the application of statistical mechanics to the study of the brain is the understanding that it, as a dynamical system, is inherently out of equilibrium. In the realm of non-equilibrium statistical mechanics and stochastic processes, the standard observable computed to determine whether a system is at equilibrium or not is the entropy produced along the dynamics. For this reason, we present here a detailed calculation of the entropy production in the Amari model, a coarse-grained model of the brain neural network, consisting of an integro-differential equation for the neural activity field, when stochasticity is added to the original dynamics. Since the way to add stochasticity is always to some extent arbitrary, particularly for coarse-grained models, there is no general prescription to do so. We precisely investigate the interplay between noise properties and the original model features, discussing in which cases the stationary state is in thermal equilibrium and which cases it is out of equilibrium, providing explicit and simple formulae. Following the derivation for the particular case considered, we also show how the entropy production rate is related to the variation in time of the Shannon entropy of the system. Full article

We propose a class of coupled dynamical systems for solving linear inverse problems, treating both the unknown variable and an auxiliary variable representing measurement dynamics as state variables. This framework does not rely on probabilistic modeling or explicit regularization; instead, it achieves noise suppression through deterministic interactions between system variables. We analyze the theoretical properties of the systems, including stability, equilibrium behavior, and convergence for the linear system, and equilibrium stability for the two nonlinear variants. The nonlinear extensions incorporate state-dependent mechanisms that preserve equilibrium stability while enhancing convergence and robustness in practice. Numerical experiments illustrate the effectiveness of the proposed approach in estimating the unknown variable and mitigating measurement noise. Full article

In this paper, we develop a delayed malaria model that integrates a discrete time delay and a non-smooth threshold-based control strategy. Using the time delay τ as a bifurcation parameter, we investigate the local stability of the endemic equilibrium through analysis of the characteristic equation. We establish sufficient conditions for the occurrence of Hopf bifurcation, demonstrating how stability switches emerge as τ varies. Furthermore, when the infected population exceeds a critical threshold I_m, a sliding mode domain arises. We analyze the dynamics within this sliding region using the Utkin equivalent control method. Numerical simulations are provided to support the theoretical findings, illustrating the complex dynamical behaviors induced by both delay and threshold control. Full article

The primary objective of this study is to provide a more precise and beneficial mathematical model for assessing corruption dynamics by utilizing non-local derivatives. This research aims to provide solutions that accurately capture the complexities and practical behaviors of corruption. To illustrate how corruption levels within a community change over time, a non-linear deterministic mathematical model has been developed. The authors present a non-integer order model that divides the population into five subgroups: susceptible, exposed, corrupted, recovered, and honest individuals. To study these corruption dynamics, we employ a new method for solving a time-fractional corruption model, which we term the q-homotopy analysis transform approach. This approach produces an effective approximation solution for the investigated equations, and data is shown as 3D plots and graphs, which give a clear physical representation. The stability and existence of the equilibrium points in the considered model are mathematically proven, and we examine the stability of the model and the equilibrium points, clarifying the conditions required for a stable solution. The resulting solutions, given in series form, show rapid convergence and accurately describe the model’s behaviour with minimal error. Furthermore, the solution’s uniqueness and convergence have been demonstrated using fixed-point theory. The proposed technique is better than a numerical approach, as it does not require much computational work, with minimal time consumed, and it removes the requirement for linearization, perturbations, and discretization. In comparison to previous approaches, the proposed technique is a competent tool for examining an analytical outcomes from the projected model, and the methodology used herein for the considered model is proved to be both efficient and reliable, indicating substantial progress in the field. Full article

In real-world applications, finite time convergence to a desired Lyapunov stable equilibrium is often necessary. This notion of stability is known as finite time stability and refers to systems in which the state trajectory reaches an equilibrium in finite time. This paper explores the notion of finite time stability in probability within the context of nonlinear stochastic dynamical systems. Specifically, we introduce sufficient conditions based on Lyapunov methods, utilizing Lyapunov functions that satisfy scalar differential inequalities involving fractional powers for guaranteeing finite time stability in probability. Then, we address the finite time optimal control problem by developing a framework for designing optimal feedback control laws that achieve finite time stochastic stability of the closed-loop system using a Lyapunov function that also serves as the solution to the steady-state stochastic Hamilton–Jacobi–Bellman equation. Full article

The issue of modeling the personal innovativeness of project team members is determined in this study. Findings from prior research on social capital associated with innovations and innovative activities reveal that social capital factors such as trust, social networks and connections, and social values determine a person’s attitude to innovations. Different connections involved in bridging (external) and bonding (internal) social capital can create conflict between project team members in different ways. To stimulate innovation in a conflict environment, a specially configured conflict management system is required that is capable of regulating the strength and intensity of the relationship between project team members. This paper analyzes the relationship between three constructs—innovativeness, social capital, and conflict. The existence of these latent constructs, which are formed by observable indicators of employees, is proven using confirmatory factor analysis (CFA). The construct of innovativeness depends on indicators such as creativity, risk propensity, and strategicity. Social capital includes observable indicators such as trust, social networks and connections, and social norms and values. Conflict consists of observable indicators of conflict between tasks, processes, and relationships. Using structural equation modeling (SEM), the causal relationship between social capital and innovativeness is substantiated with the mediating role of conflict in project groups between its participants—innovators and adaptors. The developed sociodynamic model for measuring conflict between innovators and adapters examines the required values of the controlled parameters of intra-group and inter-group connections between innovators and adapters in order to achieve equilibrium conflict dynamics, resulting in cooperation between them. This study was conducted using data from a survey of employees of a research organization. All model constructs were tested on a sample of employees as a whole, as well as for groups of innovators and adaptors separately. Full article

This paper develops a dynamic optimal growth model integrating population, economic activity, and environmental constraints to investigate sustainable long-run development. The model incorporates capital accumulation, consumption, pollution abatement, and an endogenous demographic equation in which population growth responds negatively to pollution. A critical environmental threshold is imposed beyond which population growth collapses. Calibrating the model with plausible parameter values indicates that a sustainable steady state can support a global population of approximately 5 billion, a level consistent with high per capita consumption and stable environmental conditions. The optimal policy entails devoting roughly one-third of output to pollution abatement, which is sufficient to stabilize pollution below the safe threshold without imposing excessive economic cost. In this equilibrium, the economy achieves high consumption per person, a stable capital stock, and environmental balance, thereby avoiding overshoot and collapsing scenarios. The results highlight the trade-off between economies of scale and environmental limits. Larger populations can stimulate production and innovation but risk unsustainable pollution levels, whereas smaller populations allow higher per capita welfare within ecological boundaries. These findings suggest that achieving global sustainability requires balancing population size, consumption, and ecological limits through effective pollution abatement. Full article

This study investigates the dynamic relationship between interest and noninterest income at Azer Turk Bank using quarterly data from 2016Q1–2024Q3. Unit root tests including Augmented Dickey–Fuller (ADF), Kwiatkowski–Phillips–Schmidt–Shin (KPSS), and Fourier–KPSS indicate that both variables are non-stationary in levels but become stationary after first differencing. The Hylleberg–Engle–Granger–Yoo (HEGY) test further shows that both series contain a unit root at the non-seasonal (0) frequency, while no unit roots are detected at the seasonal frequencies (π/2 and 3π/2). Johansen cointegration and the Fourier Autoregressive Distributed Lag (Fourier–ADL) framework confirm the existence of a stable long-run equilibrium. As a key methodological contribution, the study derives explicit Fourier-based Vector Error Correction Model (VECM) equations, enabling the modeling of cyclical deviations around nonlinear trends. Fourier Toda–Yamamoto and Breitung–Candelon frequency-domain causality tests reveal asymmetry: interest income consistently drives noninterest income in the short and medium run, whereas the reverse effect is weak. The results also confirm mean reversion, with deviations from equilibrium corrected within 5.9; 2.5 quarters. Overall, the findings highlight the limited diversification potential of noninterest income and the decisive role of lending in bank revenues, offering both methodological advances and practical guidance for macroprudential policy. Full article

The accurate determination of the equilibrium moisture content (EMC) of gel-related powdery samples requires strictly controlled conditions and a long time period. In this study, the adsorption and desorption isotherms of two fructooligosaccharide (FOS) powders and three inulin powders were determined using a dynamic moisture sorption analyzer at 0.1–0.9 water activity (a_w) and 20–35 °C, respectively. The adsorption and desorption isotherms all exhibited type IIa sigmoidal curves; the desorptive isotherm was smooth, the FOS adsorption curves had three inflection points, and the inulin adsorption curves had five inflection points. Large hysteresis between the adsorption and desorption isotherms occurred at 0.1–0.7 a_w for FOS and 0.1–0.6 a_w for inulin. Seven equations, Boquet, Ferro–Fontan, Guggenheim–Anderson–de Boer (GAB), Generalized D’Arcy and Watt (GDW), modified GAB (MGAB), Peleg, and our developed Polynomial, were found to fit the isotherms of the FOS and inulin samples; for adsorption, the best equations were Ferro–Fontan and GDW, and for desorption, the best equations were Polynomial and MGAB. The GDW and MGAB equations could not distinguish the effect of temperature on the isotherms, while the Polynomial equation could. The mean adsorptive monolayer moisture content (M₀) values in FOS and inulin samples were predicted as 7.29% and 7.94% wet basis, respectively. The heat of moisture sorption of FOS and inulin approached that of pure water at about 32.5% and 22.5% wet basis (w.b.) moisture content (MC), respectively. Fourier Transform Infrared Spectroscopy (FTIR) showed that the peaks in inulin with absorbance values above 0.52 and in FOS with absorbance values above 0.35 were at 1020, 1084, and 337 cm⁻¹; these could represent the amorphous structure (primary alcohol C-OH), C-O group, and hydroxyl functional group, respectively. Microscopic structure analysis showed that inulin powder particles were more round-shaped and adhered together, resulting in hygroscopic and sticky characteristics, with a maximum equilibrium moisture content (EMC) of 34% w.b. In contrast, the FOS powders exhibited irregular amorphous particles and a maximum EMC of 60% w.b. As hydrogels, 3–10% FOS or inulin addition reduced the peak, trough, final, breakdown, and setback viscosities of rice starch pasting, but increased the peak time and pasting temperature. FOS addition gave stronger reduction in the setback viscosity and in amylose retrogradation of rice starch pasting than inulin addition. The differential scanning calorimeter (DSC) showed 3–10% FOS addition reduced the amylopectin aging of retrograded paste of rice starch, but 5–7% inulin addition tended to reduce. These results suggest that FOS and inulin have strong hygroscopic properties and can be used to maintain the freshness of starch-based foods. These data can be used for drying, storage, and functional food design of FOS and inulin products. Full article

We study a stochastic differential model for the dynamics of institutional corruption, extending a deterministic three-variable system—corruption perception, proportion of sanctioned acts, and policy laxity—by incorporating Gaussian perturbations into key parameters. We prove global existence and uniqueness of solutions in the physically relevant domain, and we analyze the linearization around the asymptotically stable equilibrium of the deterministic system. Explicit mean square bounds for the linearized process are derived in terms of the spectral properties of a symmetric matrix, providing insight into the temporal validity of the linear approximation. To investigate global behavior, we relate the first exit time from the domain of interest to backward Kolmogorov equations and numerically solve the associated elliptic and parabolic PDEs with FreeFEM, obtaining estimates of expectations and survival probabilities. An application to the case of Mexico highlights nontrivial effects: while the spectral structure governs local stability, institutional volatility can non-monotonically accelerate global exit, showing that highly reactive interventions without effective sanctions increase uncertainty. Policy implications and possible extensions are discussed. Full article

This paper investigates soliton solutions of the time-fractional Biswas–Arshed (BA) equation using the Extended Simplest Equation Method (ESEM). The model is analyzed under two distinct fractional derivative operators: the $\beta$-derivative and the M-truncated derivative. These approaches yield diverse solution types, including kink, singular, and periodic-singular forms. Also, in this work, a nonlinear second-order differential equation is reconstructed as a planar dynamical system in order to study its bifurcation structure. The stability and nature of equilibrium points are established using a conserved Hamiltonian and phase space analysis. A bifurcation parameter that determines the change from center to saddle-type behaviors is identified in the study. The findings provide insight into the fundamental dynamics of nonlinear wave propagation by showing how changes in model parameters induce qualitative changes in the phase portrait. The derived solutions are depicted via contour plots, along with two-dimensional (2D) and three-dimensional (3D) representations, utilizing Mathematica for computational validation and graphical illustration. This study is motivated by the growing role of fractional calculus in modeling nonlinear wave phenomena where memory and hereditary effects cannot be captured by classical integer-order approaches. The time-fractional Biswas–Arshed (BA) equation is investigated to obtain diverse soliton solutions using the Extended Simplest Equation Method (ESEM) under the $\beta$-derivative and M-truncated derivative operators. Beyond solution construction, a nonlinear second-order equation is reformulated as a planar dynamical system to analyze its bifurcation and stability properties. This dual approach highlights how parameter variations affect equilibrium structures and soliton behaviors, offering both theoretical insights and potential applications in physics and engineering. Full article

Given the great proportion of CO₂ emissions from electricity generation in total energy-related CO₂ emissions, this article constructs a tripartite evolutionary game model consisting of vertical governments and power generation groups (PGGs), where the vertical governments include the central government (CG) and local governments (LGs), considering the externalities of different power generation modes on energy security and the environment. This article analyzes the stable strategies of the three players through replicator dynamics equations, draws the evolutionary phase diagrams, and analyzes the asymptotic stability of equilibrium points by using Jacobian matrices. To validate and broaden the results, this article also provides a numerical simulation. This article concludes that (1) a reduction in the supervision, enforcement, or low-carbonization costs of the CG, LGs, or PGGs motivates it or them to choose “supervision”, “enforcement”, or “low-carbonization” strategies; (2) an increase in penalty incomes or expenses encourages the CG or LGs to choose the “supervision” or “enforcement” strategies; (3) a rise in extra tax expenses motivates PGGs to choose the “low-carbonization” strategy; (4) a change in the externalities of energy security or the environment has no impact on the CG’s strategy. The above conclusions offer the CG and LGs with references for making effective low-carbon policies and provide PGGs with references for choosing an appropriate power generation mode. Full article

In this paper, a full-domain stochastic response analysis is performed based on the meshless method to reveal the time–frequency dynamic characteristics, including the power spectral density (PSD) responses in the frequency domain and the evolving PSD distribution in the time domain for a sandwich trapezoidal plate–shell coupled system. The general governing equations are derived based on the first-order shear deformation theory (FSDT), linear piston theory and Hamilton’s principle, and the stochastic excitation is integrated into the meshless framework based on the pseudo-excitation method (PEM). By constructing the meshless shape function covering the entire structural domain from Chebyshev polynomials and discretizing the continuous domain into a series of nodes within a square definition domain, the points are assembled according to the sequence number and the equilibrium relationship on the coupling edge to obtain the overall vibration equations. The validity is demonstrated by matching the mode shapes, PSD responses, time history displacement and critical flutter boundaries with FEM simulation and reported data. Finally, the time–frequency characteristics of each substructure under global and single stochastic excitation, and the effect of aerodynamic pressure on full-domain stochastic vibration, are revealed. Full article

This paper investigates the global dynamics of a broad class of nonlinear rational difference equations given by $x_{n+1}={\displaystyle \frac{a{x}_{n+1-2k}}{b+c{x}_{n+1-k}{x}_{n+1-2k}}},n=0,1,\dots ,$ which generalizes several known models in the literature. We establish the existence of exactly three equilibrium points and show that the trivial equilibrium is globally asymptotically stable when the parameter ratio $\alpha =(b/a)$ lies in $(-1,1)$. The nontrivial equilibria are shown to be always unstable. An explicit general solution is derived, enabling a detailed analysis of solution behavior in terms of initial conditions and parameters. Furthermore, we identify and classify minimal period $2k$ and $4k$ solutions, providing necessary and sufficient conditions for the occurrence of constant and periodic behaviors. These analytical results are supported by numerical simulations, confirming the theoretical predictions. The findings generalize and refine existing results by offering a unified framework for analyzing a wide class of rational difference equations. Full article