Search Results (395)

Persistence, coexistence, competitive exclusion, and global asymptotic stability (GAS) are closely related problems in mathematical epidemiology that are often treated by model-specific arguments. We develop a unified approach to GAS based on Perron–Volterra Lyapunov functions $L_p$, for multi-strain epidemic reaction networks. For bilinear m-strain models with irreducible rank-one infection blocks and block-diagonal next-generation structure, these functions yield a generic competitive-exclusion partition of parameter space into at most $m+1$ regions: either the disease free equilibrium is GAS, or exactly one dominant strain persists and its boundary endemic equilibrium is GAS; see non-generic tie surfaces on which the corresponding reproduction numbers coincide. We also prove a second complete GAS partition, for two-strain models with increasing concave incidence and scalar, non-interacting strain blocks, extending the Rahman–Zou result beyond rational saturating incidence. In this class, the disease-free, single-strain, and coexistence equilibria may all occur, and explicit Lyapunov functions provide the full exclusion/coexistence partition among the four possible equilibrium supports. The construction combines five ingredients: siphons, which determine forward-invariant boundary faces; triangular Jacobian structure on siphon faces; the Metzler property of transversal Jacobians and their Perron eigenvectors; regular next-generation splittings, whose spectral radii determine invasibility; and boundary transcritical invasion relays linking eigenvalue crossings to the emergence of equilibria on adjacent faces. The resulting Perron–Volterra functions combine Volterra entropy terms for resident variables with Perron-weighted linear functionals for absent strain blocks. These constructions are implemented in the Mathematica package EpidCRN, which computes siphons, transversal blocks, invasion data, Perron weights, and candidate Lyapunov functions. For the two model classes considered here, these candidates are proved to be genuine Lyapunov functions and yield complete generic GAS partitions. Full article

This paper examines the macro–micro impact of drought in South Africa using a computable general equilibrium model calibrated to the structure of the South African economy. Drought is represented as a severe supply-side shock: a 50% decline in total factor productivity in agriculture, forestry and fishing. The analysis traces how this shock is transmitted from agricultural production to prices, trade, employment, household income, consumption and welfare. The results show that agricultural output falls by 19.5%, agricultural prices rise by 43.3%, and agricultural imports increase by 84.8% as the economy shifts towards external supply. These sectoral effects generate wider macroeconomic losses, including a 1.0% decline in real GDP, a 1.7% increase in unemployment, a 1.2% fall in household income and a 1.5% reduction in household consumption. Welfare declines for both rural and urban households, but rural households experience larger losses because of their stronger dependence on agriculture, farm income, livestock assets and food markets. The findings show that drought is not only an agricultural or hydrological event; it is an economy-wide and distributional shock transmitted through production, price, trade and labour-market channels. Although imports help to cushion domestic scarcity, they do not fully offset higher prices or welfare losses. Policy responses should therefore combine drought-resilient agricultural investment, water-resource resilience, targeted social protection, food-supply stabilisation and rural livelihood diversification. Full article

High-speed turbulent boundary layers govern the transport of momentum, mass, and energy in compressible flows and play a central role in determining aerodynamic performance, skin-friction drag, aerodynamic heating, flow stability, and thermal protection requirements of advanced aerospace vehicles. Over the past three decades, direct numerical simulation (DNS) has revolutionized the study of compressible wall-bounded turbulence by resolving all dynamically relevant turbulent scales without turbulence-model assumptions, providing benchmark-quality databases and unprecedented physical insight into flow phenomena that remain difficult or impossible to measure experimentally. Together with complementary high-fidelity approaches, DNS has substantially advanced the understanding of turbulence dynamics across a broad range of supersonic and hypersonic flow conditions. This review presents a critical assessment of advances in the high-fidelity simulation of compressible turbulent boundary layers under non-reacting conditions. Particular emphasis is placed on the flow physics of canonical zero-pressure-gradient boundary layers, shock-wave/turbulent-boundary-layer interactions (SWTBLIs), pressure-gradient-driven flows, streamline-curvature effects, and thermochemical non-equilibrium phenomena. Recent developments in numerical methodologies are also briefly examined, including high-order discretization techniques, turbulence inflow generation methods, hybrid continuum-kinetic formulations, and advances in high-performance computing that have enabled DNS at increasingly high Reynolds and Mach numbers. The review highlights the major physical insights emerging from DNS studies, demonstrating that many fundamental characteristics of compressible wall turbulence remain closely related to their incompressible counterparts when appropriate compressibility transformations are employed. At the same time, DNS has revealed the critical influence of wall temperature, pressure gradients, streamline curvature, shock interactions, and finite-rate thermochemistry on turbulence structure, coherent motions, interscale energy transfer, boundary-layer separation, and aerodynamic heating. Full article

Small and medium-sized enterprises (SMEs) face increasing cyber threats, while existing cyber resilience approaches remain largely conceptual or provide static assessments with limited predictive capability. This study develops a dynamic mathematical framework for analysing and forecasting cyber resilience in SMEs. Building upon a previously developed conceptual model, the framework formalises the interactions among company security, cyber risk, cybersecurity capability, incident response and recovery, and digital maturity using normalised state variables, bounded nonlinear difference equations, and autoregressive forecasting. The theoretical analysis establishes boundedness of the state variables, equilibrium existence, and local stability of the proposed dynamic system. The framework further integrates computational resilience metrics, a Dynamic Resilience Index (DRI), scenario analysis, and sensitivity analysis within a unified analytical structure. An illustrative simulation demonstrates the computational implementation of the framework by generating resilience trajectories, supporting conditional forecasting, and comparing alternative cybersecurity scenarios. The study concludes that cyber resilience can be represented as a dynamic and measurable organisational capability. The proposed framework provides a transparent and extensible mathematical basis for continuous resilience monitoring, predictive analysis, and evidence-based cybersecurity decision-making in resource-constrained SMEs. Full article

The modern energy transition has outpaced the control and optimization frameworks built to govern it. As power and energy systems fragment into webs of renewable generators, storage operators, flexible loads, and carbon-constrained firms, the deterministic, single-optimizer models that once sufficed buckle against nonlinearity, bounded rationality, and strategic conflict among parties who learn and revise as they go. Evolutionary game theory (EGT), which traces how strategies propagate through populations by imitation and selection rather than instantaneous optimization, offers a route through this difficulty—one this review develops across three scales of low-carbon coordination central to cleaner production: enterprise-level industrial symbiosis, system-level smart energy operation, and market-level carbon governance. We synthesize three decades of theory alongside the recent fusion of EGT with artificial intelligence, where deep reinforcement learning approximates high-dimensional payoffs, federated learning lets rival firms co-train models without surrendering proprietary data, and blockchain underwrites decentralized mechanism execution. The synthesis is accompanied by two illustrative numerical case studies, constructed for this review rather than drawn from the surveyed literature, whose quantitative outputs are reported below as demonstrations of modeled behavior rather than as empirical measurements. In the first of these, cooperative emergence in industrial symbiosis hinges on critical thresholds that travel from 0.15 to 0.75 as subsidies and transaction costs vary, with anchor-enterprise targeting accelerating cooperation 2.4-fold while cutting outcome variance 3-fold. In smart energy coordination, AI-enhanced learning buys 32 to 41% faster convergence, yet pays 25 to 39% larger oscillations—a speed–stability tension whose resolution lives in a narrow learning-rate band near 0.08 to 0.12, outside which either sluggishness or instability takes hold. Carbon-market behavior turns on price thresholds: emitters switch abruptly from buying quotas toward investing in abatement once the clearing price clears firm-specific triggers, a discrete state switch that smooth equilibrium analysis misses entirely. Across all three domains, fragmented data, path dependence, and regime-switching dynamics recur as the binding constraints on modeling and on governance alike. Four mechanisms prove invariant to scale—the decisive weight of initial conditions, the catalytic leverage of well-positioned anchor agents, the equilibrium-shaping force of institutional design, and the computational reach added by AI integration—which suggests that insight earned in one domain transfers to the others. We close by mapping open problems in heterogeneity modeling, verification under deep uncertainty, and the still-unrealized coupling of digital twins with privacy-preserving learning. EGT emerges not as retrospective description but as prospective guidance for the cooperative transitions on which credible decarbonization depends. Full article

International oil price volatility poses severe risks to macroeconomic stability and energy security, presenting complex policy challenges for China as it simultaneously pursues economic growth and a low-carbon transition. To bridge the gap between general equilibrium reallocation and transition quality, this study couples an 18-sector recursive dynamic computable general equilibrium (CGE) model with a super-efficiency slacks-based measure (SBM) model to evaluate China’s macroeconomic path and green total factor productivity (GTFP) from 2023 to 2045. We simulate a permanent 200% international oil price shock starting from 2026—conceived as a tail-risk stress test—together with alternative shock scenarios of varying magnitude and persistence (P50, P100, and a five-year temporary variant of P200_5Y), and evaluate four counterfactual policies under the P200 stress-test condition: household transfers (Tran_HG), price regulation (P_REG), structural tax reduction (T_RED), and energy-transition acceleration (Delta_ENE). The shock triggers imported cost-push inflation and a regressive shift toward coal, with the long-run damage governed jointly by shock magnitude and persistence; since GTFP deteriorates monotonically with shock size, the apparent emission reductions under extreme shocks suggest a contraction-driven “efficiency illusion” rather than genuine green improvements. Individually, P_REG and T_RED are effective only as temporary shields, Tran_HG provides the strongest welfare protection but amplifies the high-carbon rebound, and Delta_ENE uniquely improves resilience and green efficiency simultaneously. Building on these results, a combined policy package (COM) is further designed and simulated, which exhibits positive complementarities; it cuts the 2026 GDP loss by about 70%, turns GDP and welfare losses into net gains by 2043 and 2040, respectively, and delivers favorable green-transition outcomes. These findings call for coordinated, phased policy packages in which fiscal space rotates from emergency shields to demand-side repair and, ultimately, to electrification-led structural transformation. Full article

This paper investigates decentralized demand-side management in renewable energy communities with limited and uncertain renewable energy resources. Consumer interactions are modeled as a Bayesian game in which self-interested consumers schedule flexible loads between daytime and nighttime periods to minimize electricity costs under time-of-use tariffs. Consumer heterogeneity is captured through private information describing both risk preferences and forecasts of renewable energy availability. Analytical conditions under which dominant strategies or mixed-strategy Bayesian Nash equilibria (BNE) exist are derived. Based on this analysis, two distributed algorithms that operate without a central coordinator are developed. The first is an iterative best-reply (BR) algorithm, while the second is a novel Demand Agreement (DA) algorithm that directly exploits the equilibrium conditions to reduce computation and communication requirements. The proposed decentralized mechanisms are compared against a centralized social-cost minimization benchmark. The results further demonstrate that the DA algorithm consistently converges to the minimum-cost equilibrium whenever a BNE exists, while requiring substantially lower communication overhead than BR. In contrast, the BR algorithm may converge even when the BNE conditions are not satisfied. Finally, the analysis quantifies the impact of consumer risk preferences and renewable generation uncertainty on BNE existence, scheduling decisions, and overall system performance. Full article

Low-altitude general aviation aircraft and unmanned aerial vehicles (UAVs) are widely deployed for complex operational tasks, yet low-altitude gusts and crosswind disturbances induce severe airspeed fluctuations, leading to variable lift, unstable flight altitude, and perturbed pitch attitude. Such aerodynamic fluctuations degrade flight smoothness and increase pilot control workload. To mitigate lift and altitude instability under unsteady incoming flow, this paper proposes a novel passive trailing-edge winglet configuration capable of self-regulating wing angle of attack (AOA) without active flight control systems. A quasi-static aerodynamic equilibrium analytical model based on moment balance about the wing pivot axis is established, combined with validated Computational Fluid Dynamics (CFD) simulations to characterize the passive AOA adjustment mechanism and quantify lift variations under velocity perturbations. Results demonstrate that the integrated wing-winglet layout generates passive aerodynamic feedback moments to automatically adjust the wing AOA when freestream speed varies. For airspeed disturbances within ±10% of the cruise velocity (102 m/s, 0.3 Ma), the total lift fluctuation of the wing-winglet assembly is suppressed within ±1.01%, whereas conventional fixed-wing configurations experience lift deviations between −16% and +22% under identical disturbance conditions. Notably, the present study only verifies quasi-static aerodynamic equilibrium under steady inflow; dynamic flight stability, unsteady aerodynamic effects, and stall-limit performance remain unexamined and require further investigation. The core novelty of this design lies in the passive negative-feedback aerodynamic moment generated by the trailing-edge winglet, which decouples fuselage attitude from wing pitching motion and stabilizes equilibrium lift under mild low-altitude gust perturbations. Full article

Glucagon-like peptide-1 (GLP-1) analogues are a major class of peptide therapeutics used to treat metabolic diseases. GLP-1-derived peptides are characterized by dynamic conformational ensembles in which folding, intermolecular assembly, and aggregation are strictly coupled processes. This study focused on the effects of sequence modifications, such as helix-promoting residues and backbone constraints on the helix-coil equilibrium, as well as lipidation, which creates competing equilibria among monomeric, oligomeric, and albumin-bound forms. These coupled equilibria simultaneously enhance pharmacokinetic properties and modulate conformational stability. We also explored how environmental conditions such as ionic concentration and temperature affect conformation, and emphasize how manufacturing processes act as external perturbations that could impact structural integrity. Moreover, we focus on the increasingly emerging new multi-agonist peptides, noting that their increased sequence complexity broadens conformational diversity and poses challenges to existing design methods. Despite significant experimental progress, predictive models capable of mapping the intricate interconnections among peptide sequences, lipidation patterns, and aggregation pathways remain critically limited. This highlights the importance of integrating biophysics, computation, and process science. The review points out that designing effective GLP-1 therapeutics rationally depends on managing conformational distributions across complex energy landscapes, not just stabilizing individual structures, in order to offer a new framework for developing the next generation of peptide drugs. Full article

Most previous computer virus propagation (CVP) models are smooth, meaning that their right-hand sides are continuously differentiable. However, recovery resources for compromised hosts are often limited, and the aggregate recovery rate may decrease once the number of bursting nodes exceeds a defense threshold. To describe this resource-constrained mechanism, this article proposes a nonsmooth susceptible–latent–bursting–susceptible (SLBS) model with a two-level recovery function and a Holling-II saturated infection rate. Well-posedness, positivity, and positive invariance of the feasible region are first proved. The basic reproduction number is derived by the next-generation matrix method, and its normalized sensitivity indices is provided. The virus-endemic equilibria are obtained by reducing the equilibrium equations to a strictly increasing scalar equation, with special attention to the threshold case at the nonsmooth switching surface. Local stability is established by piecewise linearization and explicit Routh–Hurwitz criteria. Finally, vector-graphic numerical simulations, convergence checks, and parameter robustness tests are reported. The results clarify how limited recovery capacity and saturated infection jointly affect hierarchical control of network viruses. Full article

We formulate and analyze a 26-dimensional nonlinear dynamical system governing a doubly-fed induction generator (DFIG) wind energy conversion system coupled to an infinite bus through a dynamic transmission line. Seven interacting subsystems—aerodynamics, a two-mass drivetrain, a fourth-order machine, rotor- and grid-side converter controllers, a phase-locked loop, and a pitch regulator—are assembled into a single vector field $\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x},\mathbf{u})$ on ${\mathbb{R}}^{26}$, derived in dimensionless coordinates. Strict positivity of the determinant $\mathrm{\Delta }=L_s{L}_r-L_m^2=\sigma L_s{L}_r$ for every physically admissible machine renders the flux–current map invertible, so the right-hand side is well defined; the nodal Kirchhoff constraint forms a semi-explicit differential-algebraic relation that we eliminate to obtain an explicit ordinary differential equation. The central contribution is a constructive scheme for the equilibria: the 26 stationarity conditions $\mathbf{f}({\mathbf{x}}^{\star },\mathbf{u})=\mathbf{0}$ are solved by an iterative voltage-matching procedure converging to a residual below ${10}^{-11}$ per unit—essentially machine precision—which removes the spurious start-up transients common in reported simulations. Analytically chosen feedback gains induce a hierarchy of well-separated time scales, placing the closed loop in the multiple-time-scale class; the separation is made quantitative through explicit small parameters ${\epsilon }_i$ formed from the ratios of subsystem time constants. Numerical integration of a GE $3.6$ MW configuration confirms the construction: under stationary forcing, the rotor speed stays within $1.32\times {10}^{-5}$ pu of the equilibrium, and under a large-amplitude wind program ($11\to 14\to 9$ m/s) spanning the full operating envelope, it is regulated to within $0.065\%$, while the DC-link voltage deviation remains below $2.4\times {10}^{-5}$ pu and the power balance closes with residual below ${10}^{-3}$ pu, the ≈2% mechanical–electrical gap being the modeled losses. Linearization about the computed equilibrium yields a Jacobian whose spectrum lies entirely in the open left half-plane, establishing local asymptotic stability and exposing the individual electromagnetic, torsional, and control modes. The model furnishes a rigorously initialized, analytically transparent basis for linearization, spectral stability analysis, and bifurcation study. Its practical value is that a consistent equilibrium and a certified spectrum remove the start-up transients and undocumented tuning that otherwise let initialization artifacts masquerade as genuine dynamics, so that the model can serve as a trustworthy building block for weak-grid and wind-farm stability studies. Full article

Modern multi-agent deep reinforcement learning algorithms have demonstrated empirical success in communication games, yet their black box nature precludes the analytical identification of the transition from random babbling to coordinated signalling. This study introduces an explicitly parameterised, interpretable surrogate model of belief evolution in Lewis signalling games. The proposed ordinary differential equation retains the strategic structure of cheap talk while permitting the closed-form computation of the Jacobian spectrum at the uniform babbling equilibrium. It was proven that the onset of communication corresponded to a supercritical pitchfork bifurcation with a critical threshold determined by the dissipation and sensitivity parameters. Consequently, the leading eigenvalue of the dynamics serves as a detector of the emergence point. The analytical predictions were validated through iterative simulations of Lewis signalling games, illustrating how the critical threshold dictates the consistent and stable transition from stochastic babbling to separating equilibrium. Moreover, a phenomenological experiment demonstrates a possible path toward extending spectral diagnostics to policies parameterised by neural networks in a low-dimensional setting, serving as a bridge towards potential method adaptation for general deep reinforcement learning policies, without fully validating the theoretical framework. Full article

A rod with end restraints is defined as a single-span elastic rod based on Kirchhoff’s nonlinear mechanical theory. To address the problems of unclear degrees of freedom, unsystematic boundary condition classification, and insufficient integration of theory with engineering applications, this paper establishes a systematic static analysis method. The degree of freedom of the single-span elastic rod is rigorously proved to be 12 through discrete constraint counting. Four criteria for boundary conditions are proposed: mutual correspondence and exclusion, coordination, and necessity. Based on these criteria, the boundary condition parameters are classified into generalized forces and generalized displacements, yielding 7 types with 729 valid combinations. A quaternion-based discretization method is developed to solve the equilibrium equations, and a mesh convergence study is performed using four mesh densities to confirm the numerical accuracy. The method is verified by comparing the computed results with analytical circular and helical curves, with coordinate errors below 1 cm for the circular case and below 5 cm for the helical case when using 40 elements. Using a deep-water landing string as an example, the complete application procedure is presented, including force analysis, boundary condition setting, distributed force application, and case study. The results show that the proposed model can effectively analyze three-dimensional large-deformation static problems of elastic rods, providing a unified theoretical framework for engineering applications such as cables, drill strings, and flexible manipulators. Full article

This work examines the nonlinear dynamics of a generalized Korteweg–de Vries–Zakharov–Kuznetsov equation, a model that appears in plasma physics, shallow water flows, and nonlinear wave propagation. By applying a solitary-wave transformation, the governing partial differential equation is reduced to an autonomous dynamical system, enabling a direct study of its phase portraits and equilibrium behavior. Stability of the fixed points is assessed through Jacobian matrices and eigenvalue classification, revealing parameter regimes that admit saddle states, centers, and oscillatory structures. The system’s richer behavior is explored by varying key parameters, with phase-space trajectories exhibiting periodic, quasiperiodic, and irregular wave patterns. To probe the onset of complexity, we employ several diagnostic tools, including time-series evolution, Lyapunov exponents, bifurcation analysis, sensitivity tests, and Poincaré sections, which together indicate transitions to chaotic motion. The resulting dynamics are further captured using a nonlinear autoregressive neural network, which accurately reproduces the observed trajectories. The combination of analytical and computational perspectives provides a clear framework for understanding this generalized equation and offers a practical approach for investigating other nonlinear systems with a similar structure. Full article

Rock-bed thermal energy storage (RTES) systems are attracting growing interest as low-cost, robust, and scalable sensible heat storage solutions for applications ranging from low-temperature building and greenhouse heating to medium- and high-temperature solar or waste-heat recovery systems. However, their thermo-hydraulic performance is strongly influenced by the complex interactions among heat-transfer-fluid flow, irregular rock morphology, porosity, pressure drop, interphase heat transfer, and transient thermal-front development. This review provides a focused evaluation of computational fluid dynamics (CFD) modelling strategies for packed beds of rocks, with particular attention to continuum porous-medium approaches and the closure correlations required for reliable simulation. First, the distinction between pore-scale and volume-averaged continuum modelling is discussed in terms of the trade-off between physical resolution and computational feasibility. The main pressure-drop and friction-factor correlations are then reviewed and compared, including classical packed-bed models and rock-bed-specific formulations. It is shown that hydraulic-resistance predictions are highly sensitive to particle shape, surface roughness, porosity, the bed-to-particle diameter ratio, and packing arrangement. Particle-fluid heat-transfer correlations are also examined and, when possible, converted into a consistent particle Nusselt-number form to enable direct comparison. Particular attention is given to generalized correlations, dispersion-corrected models, and air–rock-bed correlations applicable to thermal storage systems. Finally, a methodological framework for modelling RTES systems using local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) formulations is proposed. Dimensionless criteria, including the interphase thermal coupling number and particle Biot number, are introduced to support the selection between LTE and LTNE formulations. The selection of pressure-drop/friction-factor and solid–fluid heat-transfer/particle Nusselt-number correlations should be based on the similarity between the original experimental conditions and the target RTES system, and system-specific validation is recommended whenever possible. Full article