Search Results (86)

A well-known model of infectious diseases, described by a nonlinear system of delay differential equations, is investigated under the influence of stochastic perturbations. Using the general method of Lyapunov functional construction combined with the linear matrix inequality (LMI) approach, we derive sufficient conditions for the stability of the equilibria of the considered system. Numerical simulations illustrating the system’s behavior under stochastic perturbations are provided to support the thoretical findings. The proposed method for stability analysis is broadly applicable to other systems of nonlinear stochastic differential equations across various fields. Full article

In this paper, we investigate the nonlinear dynamic behavior of a cart–double pendulum system with single time delay feedback control. Based on the center manifold theorem and stochastic averaging method, a reduced-order dynamic model of the system is established, with a focus on analyzing the influence of time delay parameters and stochastic excitation on the system’s Hopf bifurcation characteristics. By introducing stochastic differential equation theory, the system is transformed into the form of an Itô equation, revealing bifurcation phenomena in the parameter space. Numerical simulation results demonstrate that decreasing the time delay and increasing the time delay feedback gain can effectively enhance system stability, whereas increasing the time delay and decreasing the time delay feedback gain significantly improves dynamic performance. Additionally, it is observed that Gaussian white noise intensity modulates the bifurcation threshold. This study provides a novel theoretical framework for the stochastic stability analysis of time delay-controlled multibody systems and offers a theoretical basis for subsequent research. Full article

This study investigates the development and sensing profile of synthetic melanin nanoparticle-coated electrodes for the electrochemical detection of heavy metals, including lead (Pb), cadmium (Cd), cobalt (Co), zinc (Zn), nickel (Ni), and iron (Fe). Synthetic melanin films were prepared in situ by the deacetylation of diacetoxy indole (DAI) to dihydroxy indole (DHI), followed by the deposition of DHI monomers onto indium tin oxide (ITO) and glassy carbon electrodes (GCE) using cyclic voltammetry (CV), forming a thin layer of synthetic melanin film. The deposition process was characterized by electrochemical quartz crystal microbalance (EQCM) in combination with linear sweep voltammetry (LSV) and amperometry to determine the mass and thickness of the deposited film. Surface morphology and elemental composition were examined using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). In contrast, Fourier-transform infrared (FTIR) and UV–Vis spectroscopy confirmed the melanin’s chemical structure and its polyphenolic functional groups. Differential pulse voltammetry (DPV) and amperometry were employed to evaluate the melanin films’ electrochemical activity and sensitivity for detecting heavy metal ions. Reproducibility and repeatability were rigorously assessed, showing consistent electrochemical performance across multiple electrodes and trials. A comparative analysis of ITO, GCE, and graphite electrodes was conducted to identify the most suitable substrate for melanin film preparation, focusing on stability, electrochemical response, and metal ion sensing efficiency. Finally, the applicability of melanin-coated electrodes was tested on in-house heavy metal water samples, exploring their potential for practical environmental monitoring of toxic heavy metals. The findings highlight synthetic melanin-coated electrodes as a promising platform for sensitive and reliable detection of iron with a sensitivity of 106 nA/ppm and a limit of quantification as low as 1 ppm. Full article

Here, we consider the stochastic graphene sheets model (SGSM) forced by multiplicative noise in the Itô sense. We show that the exact solution of the SGSM may be obtained by solving some deterministic counterparts of the graphene sheets model and combining the result with a solution of stochastic ordinary differential equations. By applying the extended tanh function method, we obtain the soliton solutions for the deterministic counterparts of the graphene sheets model. Because graphene sheets are important in many fields, such as electronics, photonics, and energy storage, the solutions of the stochastic graphene sheets model are beneficial for understanding several fascinating scientific phenomena. Using the MATLAB program, we exhibit several 3D graphs that illustrate the impact of multiplicative noise on the exact solutions of the SGSM. By incorporating stochastic elements into the equations that govern the evolution of graphene sheets, researchers can gain insights into how these fluctuations impact the behavior of the material over time. Full article

We focus on solving stochastic differential equations driven by jump processes (SDEJs) with measurable drifts that may exhibit quadratic growth. Our approach leverages a space transformation and Itô-Krylov’s formula to effectively eliminate the singular component of the drift, allowing us to obtain a transformed SDEJ that satisfies classical solvability conditions. By applying the inverse transformation proven to be a one-to-one mapping, we retrieve the solution to the original equation. This methodology offers several key advantages. First, it extends the well-known result of Le Gall (1984) from Brownian-driven SDEs to the jump process setting, broadening the range of applicable stochastic models. Second, it provides a robust framework for handling singular drifts, enabling the resolution of equations that would otherwise be intractable. Third, the approach accommodates drifts with quadratic growth, making it particularly relevant for financial modeling, insurance risk assessment, and other applications where such growth behavior is common. Finally, the inclusion of multiple examples illustrates the practical effectiveness of our method, demonstrating its flexibility and applicability to real-world problems. Full article

This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). Unlike conventional approaches relying on moment-generating functions or Fokker–Planck equations, which often yield intractable expressions, we derive explicit closed-form formulas for these moments. Our methodology leverages the Wick–Itô calculus (fractional Itô formula) and the properties of Hermite polynomials to express moments efficiently. Additionally, we establish a recurrence relation for moment computation and propose an alternative approach based on generalized binomial expansions. To validate our findings, Monte Carlo simulations are performed, demonstrating a high degree of accuracy between theoretical and empirical results. The proposed framework provides novel insights into stochastic processes with long-memory properties, with potential applications in statistical inference, mathematical finance, and physical modeling of anomalous diffusion. Full article

In this study, we aimed to develop soy protein-derived edible porous hydrogel scaffolds for cultured meat based on mechanical anisotropy to mimic the physical and biochemical properties of muscle tissues. Based on the traditional Japanese Ito-Kanten (thread agar) freeze–thaw process, we used liquid nitrogen directional freezing combined with ion crosslinking to fabricate an aligned scaffold composed of soy protein isolate (SPI), carrageenan (CA), and sodium alginate (SA). SPI, CA, and SA were dissolved in water, heated, mixed, and subjected to directional freezing in liquid nitrogen. The frozen gel was immersed in Ca²⁺ and K⁺ solutions for low-temperature crosslinking, followed by a second freezing step and lyophilization to create the SPI/CA/SA cryogel scaffold with anisotropic pore structure. Furthermore, C2C12 myoblasts were seeded onto the scaffold. After 14 d of dynamic culture, the cells exhibited significant differentiation along the aligned structure of the scaffold. Overall, our developed anisotropic scaffold provided a biocompatible environment to promote directed cell differentiation, showing potential for cultured meat production and serving as a sustainable protein source. Full article

This article presents the first theoretical analysis of the bending behavior of circular organic solar cells (COSCs). The solar cell under investigation is built on a flexible Kerr foundation and has five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. The cell is exposed to hygrothermal conditions. The related Kerr foundation lessens displacements and supports the cell. The principle of virtual work is used to generate the basic partial differential equations, which are then solved using the differential quadrature method (DQM). The results of the present theory are validated by comparing them with published ones. The effects of the temperature, humidity, elastic foundation factors, and geometric configuration characteristics on the deflection and stresses of the COSC are examined. Full article

This paper extends classical Markov switching models. We introduce a generalized semi-Markov switching framework in which the system dynamics are governed by an Itô stochastic differential equation. Of note, the optimal control synthesis problem is formulated for stochastic dynamic systems with semi-Markov parameters. Further, a system of ordinary differential equations is derived to characterize the Bellman functional and the corresponding optimal control. We investigate the case of linear dynamics in detail, and propose a closed-form solution for the optimal control law. A numerical example is presented to illustrate the theoretical results. Full article

Zinc–tin oxide (ZTO) thin films (ZnO)_x(SnO₂)_1−x with different material composition x (0 < x < 1) are deposited by spin coating on glass substrates at room temperature. The Differential Scanning Calorimetry (DSC) data of the precursor compounds show gradual phase transitions up to 480 °C. These data are used for an appropriate regime for thermal annealing of the layers. X-ray photoelectron spectroscopy (XPS) data show mixed oxide compound formation in states Zn²⁺, Sn⁴⁺ and O²⁻ of the constituents. Optical investigation manifests high transmittance above 80% in the visible spectral range and an optical band gap of 3.3–3.7 eV. The work functions vary between 4.1 eV and 5 eV, depending on the annealing, with deviations less than 1% for surface 1 mm² scans. Stack devices ITO/ZTO/metal with different metal contacts are formed. The I–V (current–voltage) measurements of the fabricated stacks exhibit Ohmic or nonlinear behavior, depending on the material composition and the work function levels. Full article

In this paper, a novel molecularly imprinted polymer membrane modified glassy carbon electrode for electrochemical sensors (MIP-OH-MWCNTs-GCE) for epinephrine (EP) was successfully prepared by a gel-sol method using an optimized functional monomer oligosilsesquioxane-Al₂O₃ sol-ITO composite sol (ITO-POSS-Al₂O₃). Hydroxylated multi-walled carbon nanotubes (OH-MWCNTs) were introduced during the modification of the electrodes, and the electrochemical behavior of EP on the molecularly imprinted electrochemical sensors was probed by the differential pulse velocity (DPV) method. The experimental conditions were optimized. Under the optimized conditions, the response peak current values showed a good linear relationship with the epinephrine concentration in the range of 0.0014–2.12 μM, and the detection limit was 4.656 × 10⁻¹¹ M. The prepared molecularly imprinted electrochemical sensor was successfully applied to the detection of actual samples of horse serum with recoveries of 94.97–101.36% (RSD), which indicated that the constructed molecularly imprinted membrane electrochemical sensor has a high detection accuracy for epinephrine in horse blood, and that it has a better value for practical application. Full article

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents $\{{\gamma }_1,{\gamma }_2,\dots \}$ under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI. Full article

This article examines the stability properties of linear stochastic difference equations with delays. For this purpose, a novel approach is used that combines the theory of inverse-positive matrices and the asymptotic methods developed by N.V. Azbelev and his students for deterministic functional differential equations. Several efficient conditions for p-stability and exponential p-stability $(2\le p<\infty )$ of systems of linear Itô-type difference equations with delays and random coefficients are found. All results are conveniently formulated in terms of the coefficients of the equations. The suggested examples illustrate the feasibility of the approach. Full article

In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonlinear models. Moreover, stability analysis and modulation instability are also studied for two types of nonlinear models in this present investigation. These analyses have several applications including analyzing control systems, engineering, biomedical engineering, neural networks, optical fiber communications, signal processing, nonlinear imaging techniques, oceanography, and astrophysical phenomena. To study nonlinear PDEs analytically, exact traveling wave solutions are in high demand. In this paper, the (1 + 1)-dimensional integro-differential Ito equation (IDIE), relevant in various branches of physics, statistical mechanics, condensed matter physics, quantum field theory, the dynamics of complex systems, etc., and also the (2 + 1)-dimensional integro-differential Sawda–Kotera equation (IDSKE), providing insights into the several physical fields, especially quantum gravity field theory, conformal field theory, neural networks, signal processing, control systems, etc., are investigated to obtain a variety of wave solutions in modern physics by using the mentioned method. Since abundant exact wave solutions give us vast information about the physical phenomena of the mentioned models, our analysis aims to determine various types of traveling wave solutions via a different integrable ordinary differential equation. Furthermore, the characteristics of the obtained new exact solutions have been illustrated by some figures. The method used here is candid, convenient, proficient, and overwhelming compared to other existing computational techniques in solving other current world physical problems. This article provides an exemplary practice of finding new types of analytical equations. Full article

An isogeometric topology optimization (ITO) model for multi-material structures under thermal-mechanical loadings using neural networks is proposed. In the proposed model, a non-uniform rational B-spline (NURBS) function is employed for geometric description and analytical calculation, which realizes the unification of the geometry and computational models. Neural networks replace the optimization algorithms of traditional topology optimization to update the relative densities of multi-material structures. The weights and biases of neural networks are taken as design variables and updated by automatic differentiation without derivation of the sensitivity formula. In addition, the grid elements can be refined directly by increasing the number of refinement nodes, resulting in high-resolution optimal topology without extra computational costs. To obtain comprehensive performance from ITO for multi-material structures, a weighting coefficient is introduced to regulate the proportion between thermal compliance and compliance in the loss function. Some numerical examples are given and the validity is verified by performance analysis. The optimal topological structures obtained based on the proposed model exhibit both excellent heat dissipation and stiffness performance under thermal-mechanical loadings. Full article