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We provide a qualitative analysis of the n-dimensional dynamical system:qi = - sum from j = 1 to n of a_(ij)/q_j~k, qi(t) > 0, i = 1,..., n, where k is an arbitrary positive integer. Under mild algebraic conditions on the constant...
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We provide a qualitative analysis of the n-dimensional dynamical system:qi = - sum from j = 1 to n of a_(ij)/q_j~k, qi(t) > 0, i = 1,..., n, where k is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix A = (a_(ij)), we show that every solution q(t), t implied by [0, a), extends to a solution on [0, +infinity), such that lim_(t -> +infinity) qi(t) = +infinity, for i = 1, ..., n. Moreover, the difference between any two solutions approaches 0 as t -> +infinity. We then use this result to give a complete qualitative analysis of a 3-dimensional dynamical system introduced by F. Gesmundo and F. Viani in modeling parabolic growth of three-oxide scales on pure metals.
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Laura, a very beautiful but also mysterious lady, inspired the famous poet Petrarch for poems, which express ecstatic love as well as deep despair.
F. J. Jones - a scientist for literary work - recognized in these changes between...
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Laura, a very beautiful but also mysterious lady, inspired the famous poet Petrarch for poems, which express ecstatic love as well as deep despair.
F. J. Jones - a scientist for literary work - recognized in these changes between love and despair an oscillating behaviour- from 1328 to 1350 - which he called Petrarch's emotional cycle.
The mathematician S. Rinaldi investigated this cycle and established a mathematical model based on ordinary differential equation: two coupled nonlinear ODEs, reflecting Laura's and Petrarch's emotions for each other, drive an inspiration variable, which coincides with Petrarch's emotional cycle. These ODEs were the starting point for the investigations in two directions: mapping the mathematical model to a suitable modelling concept, and trying to extend the model for love dynamics in modern times (F. Breitenecker et al.). This contribution introduces and investigates a modelling approach for love dynamics and inspiration by means of System Dynamics, for Laura's and Petrarch's emotions as well as for a modern couple in love. In principle, emotions and inspiration emerge from a source and are fading into a sink. But the controlling parameters for increase and decrease of emotion create a broad variety of emotional behaviour and of degree of inspiration, because of the nonlinearities. Experiments including an implementation of this model approach and selected simulations provide interesting case studies for different kinds of love dynamics - attraction, rejection and neglect - stable equilibria and chaotic cycles.
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This is a terse review of recent results on isochronous dynamical systems, namely systems of (first-order, generally nonlinear) ordinary differential equations (ODEs) featuring an open set of initial data (which might coincide wit...
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This is a terse review of recent results on isochronous dynamical systems, namely systems of (first-order, generally nonlinear) ordinary differential equations (ODEs) featuring an open set of initial data (which might coincide with the entire set of all initial data), from which emerge solutions all of which are completely periodic (i.e. periodic in all their components) with a fixed period (independent of the initial data, provided they are within the isochrony region). A leitmotif of this presentation is that 'isochronous systems are not rare'. Indeed, it is shown how any (autonomous) dynamical system can be modified or extended so that the new (also autonomous) system thereby obtained is isochronous with an arbitrarily assigned period T, while its dynamics, over time intervals much shorter than the period T, mimics closely that of the original system, or even, over an arbitrarily large fraction of its period T, coincides exactly with that of the original system. It is pointed out that this fact raises the issue of developing criteria providing, for a dynamical system, some kind of measure associated with a finite time scale of the complexity of its behaviour (while the current, standard definitions of integrable versus chaotic dynamical systems are related to the behaviour of a system over infinite time).
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Many existing dynamic systems contain mechanical effects like inertia, elasticity and friction, as well as hysteretic effects, relays, flip-flops and discrete decision makers, sensors and actuators. The effective modelling of such...
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Many existing dynamic systems contain mechanical effects like inertia, elasticity and friction, as well as hysteretic effects, relays, flip-flops and discrete decision makers, sensors and actuators. The effective modelling of such systems is essential for a thorough analysis and to improve our understanding. In general, both discrete and continuous dynamics are simultaneously in action and interact with each other. In this work, a non-linear oscillatory dynamic system, which has both continuous and discrete dynamics, is considered, and an experimental setup is constructed. For an efficient and effective analysis, the discrete and continuous dynamics are treated simultaneously using a hybrid state modelling approach. The simulations and experiments are per-formed for different conditions of the system to investigate their effect on its behaviour. The use of the hybrid state modelling approach for dynamic systems containing interacting discrete and continuous state dynamics is demonstrated both numerically and experimentally.
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In this paper, we propose a nonlinear dynamics-based framework for modeling and analyzing computer systems. Working with this framework, we use a custom measurement infrastructure and delay-coordinate embedding to study the dynami...
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In this paper, we propose a nonlinear dynamics-based framework for modeling and analyzing computer systems. Working with this framework, we use a custom measurement infrastructure and delay-coordinate embedding to study the dynamics of these comple x nonlinear systems. We findstrong indications, from multiple corroborating methods, of low-dimensional dynamics in the performance of a simple program running on a popular Intel computer—including the first experimental evidence of chaotic dynamics in real computer hardware. We also find that the dynamics change completely when we run the same program on a different type of Intel computer, or when that program is changed slightly. This not only validates our framework; it also raises important issues about computer analysis and design. These engineered systems have grown so complex as to defy the analysis tools that are typically used by their designers: tools that assume linearity and stochasticity and essentially ignore dynamics. The ideas and methods developed by the nonlinear dynamics community, applied and interpreted in the context of the framework proposed here, are a muchbetter way to study, understand, and design modern computer systems.
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We introduce the concept of homogeneous topological dynamical systems and characterise finite homogeneous topological dynamical systems. Also we discuss homogeneous dynamical systems on the real line.
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Abstract Universal Health Coverage (UHC) is one of the targets for the United Nations Sustainable Development Goal 3. The impetus for UHC has led to an increased demand for time-sensitive tools to enhance our knowledge of how heal...
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Abstract Universal Health Coverage (UHC) is one of the targets for the United Nations Sustainable Development Goal 3. The impetus for UHC has led to an increased demand for time-sensitive tools to enhance our knowledge of how health systems function and to evaluate impact of system interventions. We define the field of “health system modeling” (HSM) as an area of research where dynamic mathematical models can be designed in order to describe, predict, and quantitatively capture the functioning of health systems. HSM can be used to explore the dynamic relationships among different system components, including organizational design, financing and other resources (such as investments in resources and supply chain management systems) – what we call “inputs” – on access, coverage, and quality of care – what we call “outputs”, toward improved health system “outcomes”, namely increased levels and fairer distributions of population health and financial risk protection. We undertook a systematic review to identify the existing approaches used in HSM. We identified “systems thinking” – a conceptual and qualitative description of the critical interactions within a health system – as an important underlying precursor to HSM, and collated a critical collection of such articles. We then reviewed and categorized articles from two schools of thoughts: “system dynamics” (SD)” and “susceptible-infected-recovered-plus” (SIR+). SD emphasizes the notion of accumulations of stocks in the system, inflows and outflows, and causal feedback structure to predict intended and unintended consequences of policy interventions. The SIR?+?models link a typical disease transmission model with another that captures certain aspects of the system that impact the outcomes of the main model. These existing methods provide critical insights in informing the design of HSM, and provide a departure point to extend this research agenda. We highlight the opportunity to advance modeling methods to further understand the dynamics between health system inputs and outputs. Highlights ? Time-sensitive, dynamic models are needed to enhance understanding of health systems function. ? We define the area of health system modeling and review related literature. ? We classify literature into two categories, “system dynamics” and “susceptible-infected-recovered-plus”. ? There is opportunity to advance modeling methods to further understand the dynamics.
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We consider dynamical systems generated by continuous mappings of an interval I into itself.We prove that the trajectory of an interval J c I is asymptotically periodic if and only if Jcontains an asymptotically periodic point.
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Realistically, organizational and/or system performance is dynamic and non-linear. However, in the efficiency literature, system performance is frequently evaluated considering linear combinations of the input/output variables and...
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Realistically, organizational and/or system performance is dynamic and non-linear. However, in the efficiency literature, system performance is frequently evaluated considering linear combinations of the input/output variables and without explicitly taking into account the causes of efficiency behavior nor the dynamic behavior of systems. Policy decisions based on these results may be sub-optimized because the non-linear relationships among variables, causal relationships, and feedback mechanisms are ignored. This research takes the initial step of evaluating system performance in a dynamic environment, by relating the factors that effect system performance to the policies that govern it. To accomplish this, this paper extends the concepts of the static production axioms into a dynamic realm, where inputs are not instantaneously converted into outputs. The relationships of these new dynamic production axioms to the basic behaviors associated with system dynamics structures are explored.
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The dynamics of an atom in a strong single mode non-classical electromagnetic cavity field is studied. The reconstruction of the energy spectrum of an atom and the effect of ionization suppression in the presence of a non-classica...
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The dynamics of an atom in a strong single mode non-classical electromagnetic cavity field is studied. The reconstruction of the energy spectrum of an atom and the effect of ionization suppression in the presence of a non-classical field are discussed. It is found that a mechanism of ionization suppression similar to the Kramers-Henneberger one is also realized in strong non-classical fields. For squeezed vacuum states the threshold of the stabilization is approximately three times lower than for a classical (coherent) state of the same intensity.
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