Properties Of Dynamical Systems Research Articles

Ensemble forecasts in reproducing kernel Hilbert space family

A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a family of reproducing kernel Hilbert spaces (RKHS) with kernel functions driven by the dynamics. In the RKHS family, the Koopman and Perron–Frobenius operators are unitary and uniformly continuous. This property warrants they can be expressed in exponential series of diagonalizable bounded evolution operators defined from their infinitesimal generators. Access to Lyapunov exponents and to exact ensemble based expressions of the tangent linear dynamics are directly available as well. The RKHS family enables us the devise of strikingly simple ensemble data assimilation methods for trajectory reconstructions in terms of constant-in-time linear combinations of trajectory samples. Such an embarrassingly simple strategy is made possible through a fully justified superposition principle ensuing from several fundamental theorems.

Investigation on the Impact of Excitation Amplitude on AFM-TM Microcantilever Beam System's Dynamic Characteristics and Implementation of an Equivalent Circuit.

Alterations in the dynamical properties of an atomic force microscope microcantilever beam system in tapping mode can appreciably impact its measurement precision. Understanding the influence mechanism of dynamic parameter changes on the system's motion characteristics is vital to improve the accuracy of the atomic force microscope in tapping mode (AFM-TM). In this study, we categorize the mathematical model of the AFM-TM microcantilever beam system into systems 1 and 2 based on actual working conditions. Then, we analyze the alterations in the dynamic properties of both systems due to external excitation variations using bifurcation diagrams, phase trajectories, Lyapunov indices, and attraction domains. The numerical simulation results show that when the dimensionless external excitation g < 0.183, the motion state of system 2 is period 1. When g < 0.9, the motion state of system 1 is period 1 motion. Finally, we develop the equivalent circuit model of the AFM-TM microcantilever beam and perform related software simulations, along with practical circuit experiments. Our experimental results indicate that the constructed equivalent circuit can effectively analyze the dynamic characteristics of the AFM-TM microcantilever beam system in the presence of complex external environmental factors. It is observed that the practical circuit simulation attenuates high-frequency signals, resulting in a 31.4% reduction in excitation amplitude compared to numerical simulation results. This provides an essential theoretical foundation for selecting external excitation parameters for AFM-TM cantilever beams and offers a novel method for analyzing the dynamics of micro- and nanomechanical systems, as well as other nonlinear systems.

Non-linear model of the macroeconomic system dynamics: multiplier-accelerator

The article discusses one of the classic problems of macroeconomic dynamics, on which the neo-Keynesian theory of growth is based, so that the interaction between the multiplier and the accelerator. A new approach was proposed to develop a mathematical model of the dynamics of the mutual multiplier, which indicates the marginal propensity to save as a result of the GDP growth, and the accelerator, which reflects the growth of capital of the national income in the multiplier. The model is based on the hypothesis of non-linear dependence of the consumption on the amount of profit. This assumes that consumption growth is limited, i.e., a saturation effect occurs. In addition, the model took into account the delayed reaction of the accelerator to the influence of the multiplier. Under building the model, the considered processes were considered continuous in time. This made it possible to provide the mathematical model ”accelerator - multiplier” as a system of two differential equations of the first order. The application of the developed model to the analysis of the dynamic properties of the macroeconomic system makes it possible to evaluate the parameters at which the ”multiplier-accelerator” system enters a critical state. It has been proven that the conditions for the occurrence of self-oscillations depend on the critical value of the accelerator power. The presence of a two-fold limit cycle with corresponding ”soft” and ”hard” modes of birth (death) of the limit cycle was also founded. The applied usefulness of the model is that the choice of management decisions taking into account these results allow us preventing the occurrence of bifurcations and disasters in the process of evolution of the macroeconomic systems.

Increasing the Level of Autonomy of Control of the Electric Arc Furnace by Weakening Interphase Interactions

Steelmaking is one of the most energy-intensive industries, so improving control efficiency helps to reduce the energy used to produce a tonne of steel. Mutual influences between the phases of an electric arc furnace in available electrode movement control systems cause unproductive electrode movements as a reaction to the redistribution of currents among the phases of a three-phase power supply system due to changes in arc length in one of the phases. The nonlinearity of the characteristics of an electric arc furnace significantly complicates the ability to provide autonomous electrode movement control. The approach proposed in this paper, based on the formation of a matrix of mutual influences with variable coefficients, significantly improves the per-phase autonomy of the electrode movement control system. Nonlinear dependences of the mutual influence coefficients as a function of the current increment in the phase in which the disturbance occurred are obtained. Thus, it is possible to practically eliminate unproductive electrode movements in existing control systems by avoiding the traditional use of a dead zone, which reduces the control quality in the zone of small disturbances. The complex of experiments performed using the mathematical model demonstrate that the mutual influence improves the dynamic properties of the electrode movement system in certain operating modes.

Vibrational Spectra of Highly Anharmonic Water Clusters: Molecular Dynamics and Harmonic Analysis Revisited with Constrained Nuclear-Electronic Orbital Methods.

Vibrational spectroscopy is widely used to gain insights into structural and dynamic properties of chemical, biological, and materials systems. Thus, an efficient and accurate method to simulate vibrational spectra is desired. In this paper, we justify and employ a microcanonical molecular simulation scheme to calculate the vibrational spectra of three challenging water clusters: the neutral water dimer (H4O2), the protonated water trimer (H7O3+), and the protonated water tetramer (H9O4+). We find that with the accurate description of quantum nuclear delocalization effects through the constrained nuclear-electronic orbital framework, including vibrational mode coupling effects through molecular dynamics simulations can additionally improve the vibrational spectrum calculations. In contrast, without the quantum nuclear delocalization picture, conventional ab initio molecular dynamics may even lead to less accurate results than harmonic analysis.

Computational study of a co-infection model of HIV/AIDS and hepatitis C virus models

Hepatitis C infection and HIV/AIDS contaminations are normal in certain areas of the world, and because of their geographic overlap, co-infection can’t be precluded as the two illnesses have a similar transmission course. This current work presents a co-infection model of HIV/AIDS and Hepatitis C virus with fuzzy parameters. The application of fuzzy theory aids in tackling the issues associated with measuring uncertainty in the mathematical depiction of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been determined in this context, focusing on a model applicable to a specific group defined by a triangular membership function. Furthermore, for the model, a fuzzy non-standard finite difference (NSFD) technique has been developed, and its convergence is examined within a fuzzy framework. The suggested model is numerically validated, confirming the dependability of the devised NSFD technique, which successfully retains all of the key properties of a continuous dynamical system.

Invariant measures for substitutions on countable alphabets

Abstract In this work, we study ergodic and dynamical properties of symbolic dynamical system associated to substitutions on an infinite countable alphabet. Specifically, we consider shift dynamical systems associated to irreducible substitutions which have well-established properties in the case of finite alphabets. Based on dynamical properties of a countable integer matrix related to the substitution, we obtain results on existence and uniqueness of shift invariant measures.

Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System

A theoretically and numerically analysis on Duffing Jerk systems with a sixth-order type potential and a sixth-order potential smoothed by a gaussian function are carried out in this work. The Jerk is transformed into a dynamical system of dimension three. The dynamics and stability of the resulting system are analyzed, through phase space, bifurcation diagrams and Lyapunov exponents by varying the relevant parameters, finding the existence of a strange attractor. The dynamics of system with potential smoothed was studied by varying the smoothing parameter $\alpha$, finding that this parameter can be used to controlling chaos, since the exponential factor keeps the same fixed points and it regulates smoothly the amplitude of the potential.

Granger causality based on vector time series and quaternion algebra with possible applications to molecular dynamics data analysis.

Causal analysis plays a significant role in physics, chemistry, and biology. Dynamics of complex (bio)molecular and nanosystems, from the microscopic to the macroscopic scale, are characterized by time-dependent vectors such as positions, forces, momenta, angular momenta, or torques. Identification and analysis of causal relationships between these time-dependent signals is an important problem in the multidimensional time-series analysis and is of great practical importance in describing the properties of such dynamical systems, and to understanding their functionality. For linear stochastic systems characterized by multidimensional scalar signals, Granger proposed a simple procedure to detect causal relationships, called Granger causality. In this study we extended this formalism to vector signals representing physical vector quantities. For this purpose, we used quaternion algebra, where vector signals are treated as time-dependent quaternions. The developed analytical model is based on the autoregressive formalism. This formalism (Q-MVAR) and its numerical implementation were validated using two simple dynamic models: a rigid body model represented by a benzenelike molecular fragment, interacting with a short-range harmonic potential with a wall, as well as a system of three model atomic balls moving inside a soft spherical surface and interacting with long range electrostatic forces. Although the motivation to these studies was the analysis of classical motions in complex (bio)molecular systems, described with a mechanical model and based on molecular dynamics (MD) simulations, in particular coarse-grained ones, it should be noted that the developed extended formalism can be applied to any system composed of many rigid elements that interact with arbitrary potentials and are characterized by complex internal motions. A description of the detailed procedure for calculating causality measures is provided in the Appendicesof the Supplemental Material. This formalism and the prototype of its numerical implementation can be further developed and applied in many different fields of physical, natural, and engineering sciences.

Investigation on the 1:2:3 internal resonance of high dimensional nonlinear dynamic system for FGGP reinforced rotating pre-twisted blade under the aerodynamic forces

The study of internal resonances is one of the main research areas in nonlinear dynamics. The energy transfer behaviors between multiple vibrational modes caused by internal resonances lead to complex nonlinear vibration behaviors. In this paper, the rotating blade is modeled as a functionally graded graphene platelet (FGGP) reinforced rotating pre-twisted plate. The nonlinear vibration of a high dimensional nonlinear dynamic system for FGGP reinforced rotating pre-twisted blade under the aerodynamic forces with 1:2:3 internal resonance is investigated. The axial excitations on the blade are primarily caused by axial aerodynamic force in the tip clearance and contact forces at the top of the blade. The subsonic airflow is treated as a transverse excitation and is calculated using the vortex lattice method. Rayleigh-Ritz method is used to obtain the mode shapes of the rotating composite pre-twisted blade. The three-degree-of-freedom ordinary differential equations of the rotating FGGP reinforced pre-twisted plate are derived by using Lagrange equation. Based on the multiscale method, the averaged equations of the rotating FGGP reinforced pre-twisted plate in the case of primary resonance and 1:2:3 internal resonance under axial and transverse excitations are acquired. We present a discussion on the amplitude-frequency response, force-amplitude response, bifurcations, and chaotic motions of a rotating FGGP reinforced pre-twisted cantilever plate under both axial and transverse excitations. A crescent-shaped independent resonance region is found in the amplitude-frequency response curves. The system exhibits complex nonlinear vibration behavior as axial or transverse excitation amplitude changes.

Comparative analysis of kinetic realizations of insulin signaling

Several studies have developed dynamical models to understand the underlying mechanisms of insulin signaling, a signaling cascade that leads to the translocation of glucose, the human body’s main source of energy. Fortunately, reaction network analysis allows us to extract properties of dynamical systems without depending on their model parameter values. This study focuses on the comparison of insulin signaling in healthy state (INSMS or INSulin Metabolic Signaling) and in type 2 diabetes (INRES or INsulin RESistance) using reaction network analysis. The analysis uses network decomposition to identify the different subsystems involved in insulin signaling (e.g., insulin receptor binding and recycling, GLUT4 translocation, and ERK signaling pathway, among others). Furthermore, results show that INSMS and INRES are similar with respect to some network, structo-kinetic, and kinetic properties. Their differences, however, provide insights into what happens when insulin resistance occurs. First, the variation in the number of species involved in INSMS and INRES suggests that when irregularities occur in the insulin signaling pathway, other complexes (and, hence, other processes) get involved, characterizing insulin resistance. Second, the loss of concordance exhibited by INRES suggests less restrictive interplay between the species involved in insulin signaling, leading to unusual activities in the signaling cascade. Lastly, GLUT4 losing its absolute concentration robustness in INRES may signify that the transporter has lost its reliability in shuttling glucose to the cell, inhibiting efficient cellular energy production. This study also suggests possible applications of the equilibria parametrization and network decomposition, resulting from the analysis, to potentially establish absolute concentration robustness in a species.

Electronic, spectroscopic, dynamic and thermodynamic properties of systems formed by noble gases and oxygen

Using accurate methodologies, an extensive study was conducted to investigate the electronic, spectroscopic, dynamic, and thermodynamic properties of systems comprising noble gases (Ng) and oxygen atoms in low-lying electronic states derived from the Ng (1S) + O (3P) separated atom limits. Our target has been to obtain information complementary to that provided by previous important studies performed on such systems. The analysis of electronic energy decomposition indicates that Ng–O systems exhibit a significant non-covalent nature in the resulting bond. In terms of thermodynamics, the Ar–O and He–O systems demonstrate the highest and lowest propensity, respectively, for formation within 50–500 K. The populations of vibrational levels in the Ne–O, Ar–O, Kr–O, and Xe–O systems exhibit an inverted distribution as the temperature is increased from 50 K to room temperature and 500 K. This fact may serve as motivation for future experimental-theoretical studies, as they suggest that these systems may have possible technological applications in lasers.

СТРУКТУРНІ ЗМІНИ ЕНЕРГОСИСТЕМ ТА ВІДПОВІДНІ ЗМІНИ ЇХНІХ ДИНАМІЧНИХ ВЛАСТИВОСТЕЙ

Study results concerning the changes in the power systems (PS) dynamic properties as a result of the electrical networks' development and a significant increase of the share of distributed sources of generation in the structure of generating capacities of the PS are presented. With the use of three developed PS models which corresponded to successive stages of the PS development, as a result of information processing about electromechanical transient processes, the changes in the spectrum of PS natural frequencies as well the changes of the emergency processes' course were revealed. The obtained results make it possible to predict qualitative changes of dynamic properties of the Interconnected Power System of Ukraine at the stages of its post-war recovery and development. References 10, figures 10, tables 3.

Measurement and Modeling the Properties and Equilibrium of Fluid Systems Involving Carbon Dioxide and Hydrocarbons

On the basis of molecular dynamics modeling (MD modeling) and experimental data pVTx, a study was made of the dynamic and thermodynamic properties of a binary system based on light gases containing heavy oil (A-B). The solvent (A) used was carbon dioxide and n-alkanes (methane, ethane, and propane) in the supercritical fluid (SCF) state. Measurements of the pVTx properties were carried out in the temperature, density, and pressure ranges near the critical parameters of the light gas-heavy oil systems. Based on pVTx data and MD modeling in the A-B system, the diffusion coefficient (D) was determined near the critical parameters of the solvent. The values of D in the binary system SCF carbon dioxide or alkanes containing (methane, ethane and propane) heavy oil from the Siyazan field of Azerbaijan are calculated. The D SCF value of methane and ethane in the A-B system is higher than in a system containing SCF propane at given concentrations (c or x) of heavy oil and temperature. The value of D SCF of light gases in the A-B system increases with an increase in the concentration of heavy oil up to x = 2.5 wt. %. Diffusing molecules of SCF gases reduce the viscosity of heavy oil in the A-B system. Dependence D = f(c) tends to have an asymptotic value with increasing oil concentration. In the A-B system, the dependence of D SCF gases on pressure has a non-monotonic form. To calculate mixtures of light gases, the modified Peng-Robinson equation of state (PR EOS) was used. The isothermal dependence P-x of the carbon dioxide-methane binary system is approximated. The calculated P-x curves are consistent with the experimental ones in the temperature range 277-345 K.

A Robust Memristor-Enhanced Polynomial Hyper-Chaotic Map and Its Multi-Channel Image Encryption Application.

Nowadays, the utilization of memristors to enhance the dynamical properties of chaotic systems has become a popular research topic. In this paper, we present the design of a novel 2D memristor-enhanced polynomial hyper-chaotic map (2D-MPHM) by utilizing the cross-coupling of two TiO2 memristors. The dynamical properties of the 2D-MPHM were investigated using Lyapunov exponents, bifurcation diagrams, and trajectory diagrams. Additionally, Kolmogorov entropy and sample entropy were also employed to evaluate the complexity of the 2D-MPHM. Numerical analysis has demonstrated the superiority of the 2D-MPHM. Subsequently, the proposed 2D-MPHM was applied to a multi-channel image encryption algorithm (MIEA-MPHM) whose excellent security was demonstrated by key space, key sensitivity, plaintext sensitivity, information entropy, pixel distribution, correlation analysis, and robustness analysis. Finally, the encryption efficiency of the MIEA-MPHM was evaluated via numerous encryption efficiency tests. These tests demonstrate that the MIEA-MPHM not only possesses excellent security but also offers significant efficiency advantages, boasting an average encryption rate of up to 87.2798 Mbps.

Type series of resonant vibration equipment for concrete mixtures compaction and its main parameters calculation method

Introduction. Increasing the energy efficiency of vibration technology poses a number of challenges for its developers. A promising direction for reducing energy costs for driving vibration machines is the use of the resonance phenomenon. Due to the dynamic properties of the oscillatory system, it is possible to significantly reduce the power consumption of resonant vibration equipment, and in some cases, improve the quality of the products. The purpose of this article is to develop a standard range of resonant vibration equipment for compacting concrete mixtures and a methodology for calculating its main parameters.The object of research is the oscillatory system of a vibrating machine, consisting of two masses connected by the elastic and dissipative elements. In addition, the first mass is connected to a fixed base through elastic and dissipative elements.Materials and methods. The basic principles of theoretical mechanics, mathematical modelling and statistical processing of results were used in the research.Results. According to the research results, it was established that with an increase in the mass ratio of the oscillatory system, the dynamic coefficient decreases, and the width of the resonant zone increases. The regression equations are given. It has been established that with increasing rigidity of the working body, the dynamic coefficient decreases, and the horizontal section on the frequency response, the width of which does not change significantly, shifts to the region of higher frequencies. With an increase in the damping coefficient, the dynamic coefficient decreases, and the width of the resonant zone and the frequency range practically do not change. A wide range of nomenclature and masses of precast reinforced concrete justifies the development of a standard-size range of resonant vibration equipment. A standard range of light (up to 2 tons), medium (2-6 tons) and heavy (6-10 tons) types has been developed. Based on the analysis and generalization of research results, a method for calculating resonant vibration equipment for compacting concrete mixtures has been developed, which makes possible to increase its energy efficiency.

Computational analysis of entropy generation in three-dimensional mixed convection flow with thermal dissipation and variable thermal conductivity

Entropy generation in steady three-dimensional thermal flow is investigated under the coupled influence of viscous dissipation and mixed convection. The stretching sheet with an exponential velocity profile induces the flow. In this examination, we presume that the fluid is incompressible and possesses a Newtonian behavior and temperature-dependent thermal conductivity. Using the appropriate classical similarity variables reduces the dimensional nonlinear dynamical system of governing equations to a dimensionless nonlinear dynamical set of ordinary differential equations. It’s important to note that the selection of an exponentially varying surface temperature is deliberate, as it enables precise similarity transformations to be established in situations involving both viscous dissipation and buoyancy forces. The simplified finite difference approach (SFDM) is used to solve the acquired nonlinear dynamical set of ordinary differential equations. The tridiagonal matrix approach is used to solve the resulting system of algebraic equations. In a particular situation, the present numerical simulation is numerically checked with the previously available results and observed a good agreement. The effects of physical parameters on velocity, temperature, surface stresses and heat tranfer rate, entropy generation, and the irreversibility parameter are investigated. The entropy generation rate exhibits a decreasing trend with respect to the mixed convection parameter in the vicinity of the stretching surface. Entropy reduction can be achieved by employing a working fluid with a low Prandtl number and by minimizing the fluid friction.

Efficient Prediction of Stability Boundaries in Milling Considering the Variation of Tool Features and Workpiece Materials.

Theoretical stability analysis is a significant approach to predicting chatter-free machining parameters. Accurate milling stability predictions highly depend on the dynamic properties of the process system. Therefore, variations in tool and workpiece attributes will require repeated and time-consuming experiments or simulations to update the tool tip dynamics and cutting force coefficients. Considering this problem, this paper proposes a transfer learning framework to efficiently predict the milling stabilities for different tool-workpiece assemblies through reducing the experiments or simulations. First, a source tool is selected to obtain the tool tip frequency response functions (FRFs) under different overhang lengths through impact tests and milling experiments on different workpiece materials conducted to identify the related cutting force coefficients. Then, theoretical milling stability analyses are developed to obtain sufficient source data to pre-train a multi-layer perceptron (MLP) for predicting the limiting axial cutting depth (aplim). For a new tool, the number of overhang lengths and workpiece materials are reduced to design and perform fewer experiments. Then, insufficient stability limits are predicted and further utilized to fine-tune the pre-trained MLP. Finally, a new regression model to predict the aplim values is obtained for target tool-workpiece assemblies. A detailed case study is developed on different tool-workpiece assemblies, and the experimental results validate that the proposed approach requires fewer training samples for obtaining an acceptable prediction accuracy compared with other previously proposed methods.

Quintessential α-attractor inflation:a dynamical systems analysis

The equations for quintessential α-attractor inflationwith a single scalar field, radiation and matter in a spatially flatFLRW spacetime are recast into a regular dynamical system on acompact state space. This enables a complete description of thesolution space of these models. The inflationary attractor solutionis shown to correspond to the unstable center manifold of a deSitter fixed point, and we describe connections between slow-rolland dynamical systems approximations for this solution, includingPadé approximants. We also introduce a new method forsystematically obtaining initial data for quintessence evolution byusing dynamical systems properties; in particular, this method exploitsthat there exists a radiation dominated line of fixed points withan unstable quintessence attractor submanifold, which plays a rolethat is reminiscent of that of the inflationary attractor solutionfor inflation.

Entanglement dynamics via periodic modulations in an optomechanical system with embedded double quantum dots

In our theoretical study, we explore the dynamic behavior and entanglement properties of a hybrid optomechanical system containing double quantum dots (QDs). The system is driven by a laser with amplitude modulation and we consider the modulation of the resonance frequency of the two QDs. Through the application of modulation techniques, we can achieve the targeted mean field value and effectively control the entanglement between various degrees of freedom. This innovative approach shows great potential for the development of efficient quantum memories suitable for continuous variable quantum information processing.