Qualitative Analysis Of Dynamics Research Articles

Piecewise Dynamic Mode Decomposition of Fluid Flow Simulations

The computational simulation of fluid flows over structures still is a major research area in fluid mechanics. Because of the multiscale nature of many of the application models and consequent large amount of data, these simulations are computationally expensive, but can benefit from modern Reduced Order Models and data-driven methods. In this work, Dynamic Mode Decomposition (DMD) and its recent variation, Piecewise DMD (pDMD), are presented and compared in terms of dynamic modes extracted from the data, accuracy in reconstructing an approximation for the original dataset as a reduced order model and, most importantly, computational cost. The pDMD method is shown to be a variation of the traditional DMD that aims to improve and overcome some of the caveats of the standard version. This variation consists in decomposing the entire data into smaller datasets and applying a linear mapping independently on each one of these subsets instead of calculating a global linear fitting. Basically, it is an application of multiple DMD on small subsets instead one DMD over the whole data. Piecewise DMD is a simple and elegant idea that is based on the "divide and conquer" approach well known in the numerical analysis literature. Even though pDMD is new and should be carefully and extensively tested, it can be considered as a promising improvement over the standard DMD. The preliminary results presented in this work show how DMD can capture the dynamics and accurately reconstruct the simulation data and how pDMD can provide more accurate results when traditional DMD reaches its limitations, capture the specific dynamics of different stages of transient flows, and reduce the computational cost by 90% for a two-dimensional flow over a cylinder when compared to standard DMD. Future applications of Reduced Order Models using both DMD and pDMD include future state predictions, computationally cheap parametric simulations, and qualitative dynamic analysis of fluid flows.

The Effect of Network Delay and Contagion on Mobile Banking Users: A Dynamical Analysis

This paper analyses how network contagion affects the acceptance or rejection of mobile banking, emphasizing the risk of contagion that hinders the growth of users among bank clients. As a research method, a mathematical model based on the Susceptible, Infected, and Recovered framework is used within a nonlinear dynamic system with a distributed time delay and the optimal control strategy. The approach aims to find the behaviour dynamics of mobile banking users, non-users, and undecided ones. Our model adds value to the existing literature by employing a qualitative dynamic analysis, as opposed to other studies that study contagion empirically. The steady states and their conditions for stability are found, and the critical value for time delay causing oscillatory is determined. The optimal control strategies are identified to enlarge the number of mobile banking users and decrease the number of non-users. Numerical simulations support the theoretical findings. The research has practical implications given that the model predicts mobile banking user behaviour in assisting policy decision-making and addresses the possible policy measures that aim to increase the number of mobile banking users. The conclusions suggest that financial inclusion can contribute to the expansion of mobile banking users.

A qualitative dynamic analysis of the relationship between tourism and human development

This study analyzes the dynamic relationship between tourism and human development in a sample of 123 countries between 1995–2019 using a symbolic time series methodological analysis, with the number of international tourist arrivals per capita as the tourism measurement variable and the Human Development Index as the development measurement variable. The objective was to determine if a higher level of tourism specialization is related to a higher level of economic development. The definition of economic regime is used and the concept of the distance between the dynamic trajectories of the different countries analyzed is introduced to create a minimum spanning tree. In this way, groups of countries are identified that display similar behavior in terms of tourism specialization and levels of human development. The results suggest that countries with a high level of tourism specialization have a higher level of development as compared to those in which tourism has a lower specific weight. However, the largest group of countries identified is characterized by low levels of tourism specialization and economic development, which appears to translate into a poverty trap. Therefore, policies related to tourism activity expansion should be created since higher tourism levels have been linked to higher levels of human development. In the case of less developed countries, however, these projects should be financed by international organizations so that these countries can escape the poverty trap in which they are currently found.

Analysis of optimal lockdown in integral economic-epidemic model.

We analyze the optimal lockdown in an economic-epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends.

Qualitative analysis, chaos and coexisting attractors in an asymmetric four-well ϕ 8 -generalized Liénard oscillator driven by parametric and external excitations

In this paper, we study the qualitative dynamical analysis, routes to chaos and the coexistence of attractors in a four-well \(\phi^8\)-generalized Liénard oscillator under external and parametric excitations. The local analysis of the autonomous system reveals saddles, nodes, spirals or centers for appropriate choice of stiffness and damping coefficients. The existence of a Hopf bifurcation is proved during the stability analysis of the equilibrium points. The routes to chaos and the prediction of coexisting attractors have been investigated numerically by using the fourth order Runge-Kutta algorithm. The bifurcation structures obtained show that the system displays a rich variety of bifurcation phenomena, such as symmetry breaking, symmetry restoring, period-doubling, period windows, period-m bubbles, reverse period windows, antimonotonicity, intermittency, quasiperiodic, and chaos. In addition, remerging chaotic band attractors and remarkable routes to chaos occur in the system. Further, it is found that the system presents various coexistence of two attractors as well as the monostability and bistability phenomena. On the other hand, for large amplitude of the parametric excitation and with \(\omega = 1\), the coexistence of asymmetric periodic bursting oscillations of different topologies takes place in the system. It has also been shown numerically that for appropriate values of system parameters and initial conditions, the presented system can exhibit up to five types of coexisting multiple attractors.

Dynamics and optimal control of an online game addiction model with considering family education

<abstract><p>The problem of online game addiction among teenagers is becoming more and more serious in many parts of the world. Many of them are addicted to online games due to the lack of family education, which is an important factor that can not be ignored. To explore the optimal strategy for controlling the spread of game addiction, a new dynamic model of teenagers' online game addiction with considering family education is developed. Firstly, we perform a qualitative dynamic analysis of the model. We study the nonnegativity and boundedness of solutions, the basic reproduction number $ R_{0} $, and the existence and stability of equilibria. We then consider a model with control measures of family education, isolation and treatment, and obtain the expression of optimal control. In the numerical simulation, we study the global sensitivity analysis by the combination of Latin Hypercube Sampling (LHS) and partial rank correlation coefficient (PRCC) techniques, and show the relationship between $ R_{0} $ and each parameter. Then the forward backward sweep method with fourth order Runge-Kutta is used to simulate the control strategy in each scenario. Finally, the optimal control strategy is obtained by comparing incremental cost-effectiveness ratio (ICER) and infection averted ratio (IAR) under all strategies. The results show that with sufficient financial resources, adding the family education measures can help more teenagers avoid being addicted to games and control the spread of game addiction more effectively.</p></abstract>

Non-Linear Qualitative Dynamic Analysis of Supercritical Water-Heated Channels under External Vertical Accelerations

Employing the external force method to regard seismic impact and the three-region methodology to analyze the supercritical heated channel, a non-linear dynamic model was developed to investigate the transient characteristics of single channel or parallel channels under the impacts of vertical sinusoidal and seismic accelerations. The present model was validated against the experimental data, which could suitably estimate the additional pressure drop caused by the vertical vibrations. The influences of parameters on the seismic-induced oscillation conducted in a supercritical heated channel indicated that a longer heated length, uprating operation power and a larger outlet loss coefficient all exhibit unstable effects, while the increase of inlet loss coefficient, a larger tube diameter and a lower inlet fluid temperature would tend to stabilize the system. Moreover, the supercritical fluid would present a high natural frequency in the very small NP-SUB region. The parametric effects on the parallel channel system are related to the inherent stability nature of initial state and the interactions among channels. The more uneven heat flux distribution among channels would cause a larger vibration-induced oscillation. In particular, when it is combined with the resonance effect, the system may exhibit much larger oscillations than in the case of non-resonance.

Cooperation and Dependence in Relations between the Visegrad Four and Germany

The article examines the limits of economic independence of the Visegrad countries - Poland, Hungary, the Czech Republic and Slovakia - in their relations with Germany as the most important and influential economic partner. The author aims to trace the qualitative transformation of the relations and to discover the ways the Visegrad countries adapt their economies to the changing political, economic, social and technological realities. Methods of quantitative and qualitative dynamic analysis are used. The impact of the crisis caused by the coronavirus pandemic is considered. It is shown that the most important evidence of economic independence is trade in the categories of value added, the dynamics of the sectoral balance of mutual direct investments, as well as the signs of a mature knowledge economy. In the case of the Visegrad Group, dependence on the German economy has not disappeared, but it is moving to a different qualitative level. Based on the provisions of P. Krugman's new theory of international trade the author shows that there is a transition from vertical to predominantly horizontal intra-industry trade. Visegrad countries rely on Germany as a center for the redistribution of their value added, as well as a source of investments to the higher levels of value chains. Nevertheless, the issue of independent determination of their economic agenda is still quite acute for the Visegrad countries.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.

Detailed qualitative dynamical analysis of a cosmological Higgs field

A scalar cosmological Higgs field is expected to exist in our universe in order to create inertial mass. Some results obtained at LHC suggest that this idea must be reconsidered. The cosmological effects of scalar fields have been proposed as a mechanism to drive the evolution of the universe in various scenarios. In this paper we investigate, from the dynamical systems perspective, the evolution of a Universe consisting of a matter component $$\rho $$ together with a scalar field $$\phi $$ exhibiting a quartic polynomial self-interacting potential. We consider an homogeneous and isotropic flat Friedmann–Robertson–Walker metric. Center Manifold Theory is employed to investigate the dynamics near a non-hyperbolic critical point. We prove that there are two possible late time attractors corresponding to stable de Sitter solutions.

An Analysis of World Lavender Oil Markets and Lessons for Turkey

There has recently been an increase in lavender plantations in Turkey. More people are interested in lavender farming for essential oil production and rural tourism, and it brings many questions regarding production and marketing. Turkey is traditionally a medical and aromatic plant and essential oil producing country but has a corner in the world market only for rose oil, jasmine oil and oregano oil. Current interest in lavender production in the country has exposed a need to understand and analyse the world lavender oil markets. However, there is an information shortage and no regular dataset for world lavender oil production and trade. This study aims to consolidate information, data and expertise in order to understand and conduct a qualitative analysis of dynamics of lavender oil prices and actors in the world markets. In Turkey, almost all lavender production is from Lavandula intermedia (lavandin), as is the majority of world lavender production. Although the quantity of essential oil of lavandin traded is five times more than L. angustifolia (true lavender) oil, the most qualified and sought after lavender oil is produced from L. angustifolia. The largest lavender oil suppliers in the world are Bulgaria, France and China, and there are also many other countries which have recently increased their production. World lavender oil supply has tended to increase based on increases in plantation in Bulgaria, but quantity and quality depend on weather conditions. Demand for lavender oil, as the main driver for price determination, does not vary a lot from one year to another. However, it is expected that increases in consumer awareness towards healthier products associated with natural and organic ingredients may create an additional demand. The question is whether Turkey can become a player in the world lavender oil market. Low production costs, high profit rate and its role in rural development make lavender production attractive, but small farm sizes and a complex value chain make lavender oil production far from being economic for farmers working alone and force them to stay at the beginning of the value chain. However, as there will always be a place in the market for quality lavender oil, Turkey should focus on quality and organization of lavender value chain in order to be competitive in the world market.

The dynamical roles of miR-17-92 on the E2F-related network during the G1/S transition

E2F is a key transcription factor in the cell cycle network that regulates cell transition from G1 to S phase. MiR-17-92 plays an important role in the expression of E2F and regulates the progression of the cell cycle. Based on the Rb-E2F-MiR cell cycle network, we found that introduction of miR-17-92 in the network prolongs the cell cycle transition from G1 to S phase effectively and also maintains the robustness of the network against fluctuations. The dynamics of E2F are highly nonlinear, and by analysis of the bifurcation diagrams, we found that depending on the strength of interaction between E2F, microRNA and Myc, the expression level of E2F and miR-17-92 established is forward or antiphase synchronization. Moreover, through qualitative dynamic analysis and the quantitative Pearson coefficient, ‘miRNA-target avoidance,’ i.e., the relationship between miR-17-92 and E2F has been discovered in the noisy system. These results may help in further scrutiny and understanding the dual nonlinear role of miR-17-92 in many other vital biology processes.

Pathophysiology of Degenerative Mitral Regurgitation: New 3-Dimensional Imaging Insights.

Despite its high prevalence, little is known about mechanisms of mitral regurgitation in degenerative mitral valve disease apart from the leaflet prolapse itself. Mitral valve is a complex structure, including mitral annulus, mitral leaflets, papillary muscles, chords, and left ventricular walls. All these structures are involved in physiological and pathological functioning of this valvuloventricular complex but up to now were difficult to analyze because of inherent limitations of 2-dimensional imaging. The advent of 3-dimensional echocardiography, computed tomography, and cardiac magnetic resonance imaging overcoming these limitations provides new insights into mechanistic analysis of degenerative mitral regurgitation. This review will detail the contribution of quantitative and qualitative dynamic analysis of mitral annulus and mitral leaflets by new imaging methods in the understanding of degenerative mitral regurgitation pathophysiology.

Qualitative dynamical analysis of chaotic plasma perturbations model

In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov–Takens, Andronov–Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

Qualitative analysis of dynamics in Kolmogorov’s problem on a flow of a viscous incompressible fluid

We numerically analyze the qualitative behavior of solutions in the two-dimensional problem on a periodic flow of a viscous incompressible fluid with an exciting force (the Kolmogorov problem). To construct an approximate solution, we use the Bubnov–Galerkin method based on spline approximations. We prove the convergence of the method to the solution of the problem in the weak sense. We compare the obtained results with the results of other authors as well as with the Galerkin method based on trigonometric polynomials and with a hybrid finite-volume finite-element method. We carry out a bifurcation analysis of the problem and indicate a scenario of passage from regular solutions to chaotic ones.

STRUCTURAL PRINCIPLES FOR COMPLEX DYNAMICS IN GLASS NETWORKS

Gene-regulatory networks are potentially capable of more complex behavior than convergence to a stationary state, or even cycling through a simple sequence of expression patterns. The analysis of qualitative dynamics for these networks is facilitated by using piecewise-linear equations and its state transition diagram (an n-dimensional hypercube, in the case of n genes with a single effective threshold for the protein product of each). Our previous work has dealt with cycles of states in the state transition diagram that allow periodic solutions. Here, we study a particular kind of figure-8 pattern in the state transition diagram and determine conditions that allow complex behavior. Previous studies of complex behavior, such as chaos, in such networks have dealt only with specific examples. Our approach allows an appreciation of the design principles that give rise to complex dynamics, which may have application in assessing the dynamical possibilities of gene networks with poorly known parameters, or for synthesis or control of gene networks with complex behavior.

Structural principles for periodic orbits in glass networks

A piecewise-linear differential equation model framework for gene regulatory interactions (Glass networks) has allowed considerable analysis of qualitative dynamics in such systems, including periodicity, an important class of regulatory behaviors. Here, we present new results relating the structure of the network to its dynamics (structural principles). The structure we refer to is the state space of the network, which is a digraph on an n-cube in the case of a single threshold per gene. In particular, we show that for a wide class of cycles in the state space there exist parameter values, consistent with the graph structure, for which a periodic orbit exists in the network. For some classes, we show in addition that stable periodic orbits exist. These results extend greatly earlier work by Glass and Pasternack (J Math Biol 6:207-223, 1978).

Financial fragility and economic fluctuations

This paper proposes a simple prototype model that describes the complex dynamics of a sophisticated monetary economy. The interaction between the current and intertemporal financial constraints on economic units brings about irregular fluctuations at both micro and macro levels. We use qualitative dynamic analysis and numerical simulations to investigate the interaction between financial fragility, modeled in terms of structural instability, and dynamically unstable financial fluctuations. The model, suggested recently by one of the authors, is here reformulated in more operational terms and extended in a number of new directions.

An Algorithmic Approach to Chain Recurrence

In this paper we give a new definition of the chain recurrent set of a continuous map using finite spatial discretizations. This approach allows for an algorithmic construction of isolating blocks for the components of Morse decompositions which approximate the chain recurrent set arbitrarily closely as well as discrete approximations of Conley’s Lyapunov function. This is a natural framework in which to develop computational techniques for the analysis of qualitative dynamics including rigorous computer-assisted proofs.

Isotropic singularity in inhomogeneous brane cosmological models

We discuss the asymptotic dynamical evolution of spatially inhomogeneous brane-world cosmological models close to the initial singularity. By introducing suitable scale-invariant dependent variables and a suitable gauge, we write the evolution equations of the spatially inhomogeneous G2 brane cosmological models with one spatial degree of freedom as a system of autonomous first-order partial differential equations. We study the system numerically, and we find that there always exists an initial singularity, which is characterized by the fact that spatial derivatives are dynamically negligible. More importantly, from the numerical analysis we conclude that there is an initial isotropic singularity in all these spatially inhomogeneous brane cosmologies for a range of parameter values which include the physically important cases of radiation and a scalar field source. The numerical results are supported by a qualitative dynamical analysis and a calculation of the past asymptotic decay rates. Although the analysis is local in nature, the numerics indicate that the singularity is isotropic for all relevant initial conditions. Therefore this analysis, and a preliminary investigation of general inhomogeneous (G0) models, indicates that it is plausible that the initial singularity is isotropic in spatially inhomogeneous brane-world cosmological models and consequently that brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place.