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Two different control methods are proposed in this paper to effectively control the chaotic phenomenon of nonlinear dynamical system. One is a new Hamilton energy feedback control method based on Helmholtz’s theorem, which reduces the Lyapunov exponents value of the system by adjusting the feedback gain for controlling chaos. The other is to control the chaos of the system by using delayed feedback control method. Based on this method, we consider the local asymptotic stability of the equilibrium point of the system, and give conditions for the existence of the Hopf bifurcation of the system and the stability domain of the delay parameters. By using the centre manifold theorem and the Poincare normal form method, specific formulas for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions are derived. Finally, the simulation results show that chaos can be controlled by choosing appropriate time-delay parameters.

This paper explores the evolution of gravastars within the context of the Lyra geometry. The mathematical formulations of the three regions of a gravastar: (i) the inside region, (ii) the shell region and (iii) the external void region are described separately, along with their physical characteristics and graphical representations. The study explores different aspects of our model by analysing the behaviour of physical parameters. It solves the modified Einstein’s field equations, which are derived from this geometry, under the conditions of gravastar formation. The investigation focusses on the physical properties of the shell region, such as energy density, proper length, full energy, entropy, surface tension, thinness and energy conditions. Additionally, the stability of the gravastar model is examined by analysing the surface red-shift in relation to the shell length.

Computer model has been extensively adopted to overcome the time limitation of language evolution by transforming language theory into physical modelling mechanism, which helps to explore the general laws of evolution. In this paper, a model is designed to simulate the evolution process of languages in human settlements, with the associated network topology being lattice. The language of each node in the lattice will evolve gradually under the influence of its own fixed evolutionary direction and neighbours. According to the computational experiment results, it is discovered that the state points of languages always converge into several clusters during the evolution process, which gives us an insight into language evolution.

This article presents an analysis and control approach for a non-smooth air-gap permanent magnet synchronous motor (NSAG-PMSM) in the absence of external disturbances. The analytical study of NSAG-PMSM shows the existence of equilibrium points. Based on the Routh–Hurwitz criterion, the stability of the equilibrium points reveals the existence of transcritical bifurcation. NSAG-PMSM exhibits various dynamical behaviours, such as bistable chaos, periodic spiking oscillations, chaotic spiking characteristics, coexistence between periodic and chaotic behaviours and periodic evolution towards monostable chaos as system parameters change. The research uses microcontroller implementation to validate the dynamical characteristics observed during the numerical simulations of the NSAG-PMSM. The study of NSAG-PMSM proposes a strategy to mitigate chaos and stabilise the system using two simple controllers, with a comparative study presented using peak overshoot and settling time diagrams. By combining these different aspects, this article significantly contributes to the understanding of the operation in NSAG-PMSM, highlighting specific aspects related to the application of microcontroller techniques in the field of electrical engineering and solutions to chaos control.

In this paper, we study the travelling wave parametric amplifier-superconducting nonlinear asymmetric inductive element (TWPA-SNAIL) transmission line circuit equation and its variable coefficients form, which may describe transmission line circuits for travelling wave parametric amplifiers including superconducting nonlinear asymmetric inductive elements. We derive some exact solutions, including dark soliton, bright soliton, periodic, trigonometric function and hyperbolic function solutions using Jacobi elliptic function expansion method. The soliton solutions of this circuit equation are useful to analogue black–white hole event horizon pairs. To better describe the dynamical behaviour of these solutions, we plot three-dimensional density and two-dimensional images. By varying the parameters, we find that some parameters have an effect on the structure of the solution. In addition, for the variable coefficient equations, we present images containing trigonometric and exponential functions in the solution and obtain some satisfactory results by comparing the graphs with the coefficient functions. The results show that the Jacobi elliptic function expansion method is a remarkable, direct and desirable method for solving a class of nonlinear partial differential equations.

Aerospace research is increasingly focusing on propulsion system analysis. Heat transmission at high temperatures controlled by thermal radiation is used in spaceship propulsion systems. Hence, the current work investigates the magneto-Williamson nanofluid peristalsis flow in relation to thermal effect and slip-boundary circumstances with double-diffusion convection. In the flow's opposite direction, a steady, static magnetic field is applied. A mathematical model with appropriate boundary conditions is built by considering the momentum, continuity and energy equations. By considering the long wavelength and low Reynold estimation, the resulting equations are further made simpler. Then a numerical solution to the resulting reduced partial differential equations is obtained. Finally, there is a visual representation of the non-Newtonian propelling flow parameters, which include the Brinkman number, Prandtl number, Hartmann number, radiation parameter, particle volume fraction, electric field and slip parameters. It is highlighted that enhancing the coefficient of thermophoresis strengthens the temperature contour because increasing the number of particles merged enhances thermophoretic power. Furthermore, because of the substantial migration of nanoparticles from a heated region to a cooled one, the distribution of concentration becomes less cumbersome. It is also revealed that the fraction of nanoparticles rises because of rising thermal radiation and Brownian motion because nanofluids have a significant temperature distribution that may affect the system's distribution.

The radiation impact on the thermal distribution of the radial fin with the temperature-dependent thermal conductivity is discussed in this paper. The basic governing heat equation of the radial fin is formulated with the assistance of the Fourier law of heat conduction. The dimensional heat equation of the radial fin is non-dimensionalised utilising appropriate dimensionless variables and this ordinary differential equation (ODE) is tackled by employing the physics-informed neural network (PINN) scheme. The thermal attributes of the radial fin are investigated for different parameters like convection–conduction parameter, radiation–conduction parameter and thermal conductivity parameter. The outcomes of the systematic assessments of these parameters are demonstrated with the support of graphs. The rise in the thermal conductivity variable promotes thermal variation in the fin. A decrease in radiative–conductive variable scales augments the temperature dispersal through the fin. Furthermore, PINN incorporates physics equations directly into its architecture, unlike standard numerical approaches, which frequently require extensive mathematical expertise for accuracy. This approach enables PINN to give precise findings even when working with minimal training data, saving substantial time and resources.

Modifying electrical and optical properties in two-carbon materials is essential for electronic devices, energy storage and biosensor applications. We report a comparative study of the effect of systematically intercalated strontium atoms in AA- and AB-stacked bilayer graphene (BG) in the framework of density functional theory (DFT). The electronic band structures, the total and partial electronic density of states and the dielectric function are studied. We show that the intercalation of atoms can influence both electronic properties. Our results show that the Dirac cones, a signature of graphene, are translated into the conduction band. This property may be useful in band-gap tuning applications of nanodevices. The optical properties were calculated parallel and perpendicular to the graphene sheet under polarised electric fields. The calculated optical properties show that the intercalation of Sr in the AA- and AB-stacked BGs promotes IR absorption. The findings provide a basis for developing graphene intercalary compounds, which can be used in optoelectronics to control the absorption of light wavelengths and specifically in biosensor applications.

Oxygen packing factor (OPF) and atomic-level structure characteristics of the germania system at high temperature and pressure were investigated based on molecular dynamics (MD) simulation. Data analytic techniques, including Monte Carlo method, machine learning and data mining, were used to gain insights from the simulation data. We focus on elucidating the correlation between structure and OPF under high pressure. The research results have established the relationship of the network structure, polyamorphism, liquid–liquid phase transformations and microphase separation with OPF. The research findings revealed promising possibilities in developing novel materials and their applications.

The impact of magnetic field on the peristaltic motion of alumina/water ((mathrm Al_2O_3/H_2O)) and alumina/ethylene glycol ((mathrm Al_2O_3/C_2H_6O_2)) nanofluids in a vertical asymmetrical channel with mass/heat transfer was examined in this study. Unsteady governing equations were derived for the present problem. The Galilean transformation was used to transform the unsteady governing equations into steady ones. Reducing partial differential equations yields ordinary differential equations with the implementation of the long wavelength and low Reynolds number approximations. Coupled nonlinear differential equations (concentration and temperature equations) were solved analytically using the perturbation technique. In a similar fashion, the exact solution to the stream function is computed. MATLAB software was used to plot temperature, pressure rise, velocity and concentration, while MATHEMATICA software was used for generating streamlines. The findings suggest that, in comparison to the (mathrm Al_2O_3/H_2O) nanoliquid, the velocity profile for the (mathrm Al_2O_3/C_2H_6O_2) nanoliquid shows significantly larger magnitudes.