Framework Of Nonlinear Dynamics Research Articles

Boardroom tenure, financial expertise and bank performance: a nonlinear dynamic framework

ABSTRACT This research investigates the influence of boardroom tenure and financial expertise on US bank performance in a nonlinear dynamic framework. To this aim, we utilize a sample of 305 banks during the 2010–2021 period, and we implement three empirical methodologies: GMM analysis, threshold technique, and quantile approach. Our findings reveal that the individual and interaction effects of boardroom financial expertise and tenure on bank performance are positive. Also, we provide evidence of an inverted U-shaped relation between boardroom tenure and bank performance, and between the board’s financial expertise and bank performance. Moreover, threshold analysis shows the presence of threshold effects in the relationship between boardroom tenure, expertise, and performance. Quantile results demonstrate that boardroom financial expertise improves the performance of high-performing banks. In contrast, boardroom tenure enhances the performance of low-performing banks but diminishes the performance of their high-performing counterparts.

Thermodynamic and dynamical predictions for bifurcations and non-equilibrium phase transitions

“Critical transitions”, in which systems switch abruptly from one state to another are ubiquitous in physical and biological systems. Such critical transitions in complex systems are commonly described as dynamical processes within the framework of nonlinear dynamics and the bifurcation theory. However, systematic treatment from the global thermodynamic perspective is still challenging. Furthermore, from the previous established dynamical framework, a universal early-warning signal for predicting such transitions is still not very clear and complete. Here we developed a non-equilibrium thermodynamic and dynamical framework for general complex systems. Our approach used the analogy to the conventional statistical mechanical treatment for the equilibrium phase transitions, while the nature of the non-equilibrium dynamics is still captured and reflected. Applying this framework to two well-known non-equilibrium systems, we found warning signals based on thermodynamic quantities and the time-reversal symmetry breaking nature of non-equilibrium systems can be detected much earlier than those explored in the previous works based on nonlinear dynamics and the bifurcation theory. Irreversibility of the observed time series strongly correlates to the behavior of these thermodynamic quantities and provides a practical way for predicting transitions. Our work provides a general yet practical approach for exploring collective behaviors in complex systems.

A sparse optimal closure for a reduced-order model of wall-bounded turbulence

In the present study, a set of physics-informed and data-driven approaches are examined towards the development of an accurate reduced-order model for a turbulent plane Couette flow. Based on the utilisation of the proper orthogonal decomposition (POD), a particular focus is given to the development of a reduced-order model where the number of POD modes are not large enough to cover the full dynamics of the given turbulent state, the situation directly relevant to the reduced-order modelling for turbulent flows. Starting from the conventional Galerkin projection approach ignoring the truncation error, three approaches enhanced by both physics and data are examined: (1) sparse regression of the POD-Galerkin dynamics; (2) Galerkin projection with an empirical eddy-viscosity model; (3) Galerkin projection with an optimal eddy viscosity obtained from a newly proposed sparse regression – an idea applying the sparse identification of nonlinear dynamics framework to an eddy-viscosity model. The sparse regression of the POD-Galerkin dynamics does not perform well, as the number of POD modes for the given chaotic dynamics appears to be too small. While the unsatisfactory performance of the Galerkin projection model with an empirical eddy viscosity is observed, the newly proposed approach, which combines the concept of an optimal eddy-viscosity closure with a sparse regression, more accurately approximates the chaotic dynamics than the other reduced-order models considered. This is demonstrated with the mean and time scales of the POD mode amplitudes as well as the first- and second-order turbulence statistics.

Modeling nonlinear beams for metamaterials design in a dynamic setting

We present, in a nonlinear dynamic framework, a beam model suitable for metamaterials design. The beam model, formulated directly in a discrete way, is completely defined by means of the strain and the kinetic energies. Differently from Hencky’s seminal work, which only considers flexibility for computing buckling loads for rectilinear Euler–Bernoulli beams, the proposed model considers both the extensibility and shearability strain energy contributions along with translational and rotational kinetic energy contributions. All the derivations are carried out in a three-dimensional setting and successively particularized to the two-dimensional case. After having coded the proposed discrete model into an efficient time-step analysis strategy, its performances have been assessed by means of some numerical simulations for a simple auxetic cell.

Dynamics of Gap-leaping Western Boundary Currents with Throughflow Forcing

AbstractThe dynamics of gap-leaping western boundary currents (e.g. the Kuroshio intrusion, the Loop Current) are explored through rotating table experiments and a numerical model designed to replicate the experimental apparatus. Simplified experimental and numerical models of gap-leaping systems are known to exhibit two dominant states (leaping or penetrating into the gap) as the inertia of the current competes with vorticity constraints (in this case the β-effect). These systems are also known to admit multiple states with hysteresis. To advance towards more realistic oceanographic scenarios, recent studies have explored the effects of islands, mesoscale eddies, and variable baroclinic deformation radii on the dynamical system. Here, the effect of throughflow forcing is considered, with particle tracking velocimetry (PTV) used in the lab experiments. Mean transport in or out of the gap is found to significantly shift the hysteresis range as well as change its width. Because of these transformations, changes in throughflow can induce transitions in the gap-leaping system when near a critical state (leaping-to-penetrating/ penetrating-to-leaping). Results from the study are interpreted within a nonlinear dynamical framework and various properties of the system are explored.

Novel Nonlinear Dynamic Beam–Foundation Interaction Model

A nonlinear dynamic framework for the analysis of beam–foundation interaction is developed. The extended Hamilton’s principle is used to analyze the response of Euler–Bernoulli beams vibrating on nonlinear continuums (e.g., soils) and subjected to vibrating and moving loads. The continuum beneath the beam is characterized by a nonlinear elastic constitutive relationship that connects the secant shear modulus to the induced strain. The novel feature of the analysis is that the nonlinear compression and shear parameters ks and ts of the continuum (i.e., foundation) do not have to be assumed a priori, as is required in conventional beams on foundation analysis, and are obtained as part of the solution. In fact, it is shown that these parameters are not constant but change with time and depend on the beam–foundation interaction. Another novel feature of the analysis is that the mass of the foundation participating in the vibration is obtained as part of the solution and does not have to be assumed a priori. Thus, the analysis rigorously takes into account the nonlinear beam–foundation (soil–structure) interaction within a dynamic time-integration framework. The developed framework is as accurate as and about 50% faster than conventional nonlinear dynamic finite element analysis. Inputs to the analysis can be given in the form of a text file without any requirement of numerical mesh generation, making the approach rather user friendly. The characteristics of the developed nonlinear dynamic foundation model are illustrated through examples of moving and vibrating loads.

Co-movement and Dynamic Correlation of Financial and Energy Markets: An Integrated Framework of Nonlinear Dynamics, Wavelet Analysis and DCC-GARCH

In this paper, we analyze the inherent evolutionary dynamics of financial and energy markets. We study their inter-relationships and perform predictive analysis using an integrated nonparametric framework. We consider the daily closing prices of BSE Energy Index, Crude Oil, DJIA Index, Natural Gas, and NIFTY Index representing natural resources, developing and developed economies from January 2012 to March 2017 for this purpose. DJIA and NIFTY account for the global financial market while the other three-time series represent the energy market. First, we investigate the empirical characteristics of the underlying temporal dynamics of the financial time series through the technique of nonlinear dynamics to extract the key insights. Results suggest the existence of a strong trend component and long-range dependence as the underlying pattern. Then we apply the continuous wavelet transformation based multiscale exploration to investigate the co-movements of considered assets. We discover the long and medium-range co-movements among the heterogeneous assets. The findings of dynamic time-varying association reveal interesting insights that may assist portfolio managers in mitigating risk. Finally, we deploy a wavelet-based time-varying dynamic approach for estimating the conditional correlation among the said assets to determine the hedge ratios for practical implications.

Complex Structure in Modified Henon Map and Its Dynamic Evolution

Strange evolutionary behaviours of modified discrete Henon map investigated in the framework of non-linear dynamics. The study carried out to visualise regular and chaotic evolutions and to study the complexity in the system. Bifurcation diagrams obtained by varying a parameter while keeping other parameter fixed. Regular and chaotic attractors are drawn for different sets of parameters. During this process a multifold strange attractor also emerged for certain pair of parameters. Numerical calculations performed to calculate Lyapunov exponents for regular and chaotic cases. In order to measure complexity in the system calculations further extended to obtain the topological entropies for sets of parameter values. Finally, correlation dimensions of chaotic attractors obtained with proper description of numerical setup. Results obtained are significant and presented through graphics.

On the Convergence of the SINDy Algorithm

One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the simplest representation (i.e. the smallest amount of terms). One such approach is the sparse identification of nonlinear dynamics framework [6] which uses a sparsity-promoting algorithm that iterates between a partial least-squares fit and a thresholding (sparsity-promoting) step. In this work, we provide some theoretical results on the behavior and convergence of the algorithm proposed in [6]. In particular, we prove that the algorithm approximates local minimizers of an unconstrained $\ell^0$-penalized least-squares problem. From this, we provide sufficient conditions for general convergence, rate of convergence, and conditions for one-step recovery. Examples illustrate that the rates of convergence are sharp. In addition, our results extend to other algorithms related to the algorithm in [6], and provide theoretical verification to several observed phenomena.

A two-phase single-reciprocating-piston heat conversion engine: Non-linear dynamic modelling

A non-linear dynamic framework is presented for the modelling of a novel two-phase heat engine termed ‘Up-THERM’, which features a single solid moving-part (piston). When applied across the device, a constant temperature difference between an external (low- to medium-grade) heat source and an external heat sink is converted into sustained and persistent oscillations of pressure and volumetric fluid displacement. These oscillations are transformed in a load arrangement into a unidirectional flow from which power is extracted by a hydraulic motor. The Up-THERM engine is modelled using a system of first-order differential equations that describe the dominant thermal/fluid processes in each component of the device. For certain components where the deviations from a linear approximation are non-negligible (gas spring in the displacer cylinder, check valves and piston valve, and heat exchangers), a non-linear description is employed. A comparison between the linear and non-linear descriptions of the gas spring at the top of the displacer cylinder reveals that the non-linear description results in more realistic predictions of the oscillation frequency compared to experimental data from a similar device. Furthermore, the shape of the temperature profile over the heat-exchanger surfaces is modelled as following a hyperbolic tangent function, based on findings from an experimental investigation. Following the validation of these important device components, a parametric study is performed on the Up-THERM engine model with the aforementioned non-linear component descriptions, aimed at investigating the effects of important geometric parameters and of the heat-source temperature on key performance indicators, namely the oscillation frequency, power output and exergy efficiency of the engine. The results indicate that the geometric design of the displacer cylinder, including the height of the gas spring at the top of the cylinder, and the heat-source temperature have the most significant influence on the performance of the engine. A maximum exergy efficiency of 2.8% and a maximum power output of 175W are observed at the proposed operating temperature of 450°C for a nominal Up-THERM design (based on the physical dimensions of a device prototype and water as the working fluid; the role of the working fluid is explored in follow-up paper Ref. [1]) but with shorter displacer cylinder gas-spring lengths relative to a nominal design. The results and insight can assist the further development of this technology, in particular as a prime mover in combined heat and power applications.

New Perspectives on Spontaneous Brain Activity: Dynamic Networks and Energy Matter.

Spontaneous brain activity has received increasing attention as demonstrated by the exponential rise in the number of published article on this topic over the last 30 years. Such “intrinsic” brain activity, generated in the absence of an explicit task, is frequently associated with resting-state or default-mode networks (DMN)s. The focus on characterizing spontaneous brain activity promises to shed new light on questions concerning the structural and functional architecture of the brain and how they are related to “mind”. However, many critical questions have yet to be addressed. In this review, we focus on a scarcely explored area, specifically the energetic requirements and constraints of spontaneous activity, taking into account both thermodynamical and informational perspectives. We argue that the “classical” definitions of spontaneous activity do not take into account an important feature, that is, the critical thermodynamic energetic differences between spontaneous and evoked brain activity. Spontaneous brain activity is associated with slower oscillations compared with evoked, task-related activity, hence it exhibits lower levels of enthalpy and “free-energy” (i.e., the energy that can be converted to do work), thus supporting noteworthy thermodynamic energetic differences between spontaneous and evoked brain activity. Increased spike frequency during evoked activity has a significant metabolic cost, consequently, brain functions traditionally associated with spontaneous activity, such as mind wandering, require less energy that other nervous activities. We also review recent empirical observations in neuroscience, in order to capture how spontaneous brain dynamics and mental function can be embedded in a non-linear dynamical framework, which considers nervous activity in terms of phase spaces, particle trajectories, random walks, attractors and/or paths at the edge of the chaos. This takes us from the thermodynamic free-energy, to the realm of “variational free-energy”, a theoretical construct pertaining to probability and information theory which allows explanation of unexplored features of spontaneous brain activity.

VFA robust control of an anaerobic digestion pilot plant: experimental implementation

In this work, an experimental implementation of a model based output feedback (OF) scheme applied to regulate the volatile fatty acids concentration of an anaerobic digestion pilot plant is presented. The OF scheme was developed within a global nonlinear dynamics framework, resulting in an interlaced control-observer design in the light of passivity, observability, and bifurcation properties. From a industrial control perspective, the resulting OF scheme is a saturated PI controller with: (i) systematic construction and tuning and (ii) nonlocal robust stability conditions in terms of control gains and limits. Experimental results demonstrate the applicability, robustness and reliability of the OF control scheme in a real environment under several load disturbances, severe uncertainties and typical operational failures.

A practical nonlinear dynamic framework for solving a class of fractional programming problems

In this paper, we present a high-performance dynamic optimization scheme to solve a class of fractional programming (FP) problems. The main idea is to convert the FP problem into an equivalent convex second-order cone programming problem. A neural network model based on a dynamic model is then constructed for solving the obtained convex programming problem. By employing a credible Lyapunov function approach, it is shown that the proposed neural network model is stable in the sense of Lyapunov and is globally convergent to an exact optimal solution of the original optimization problem. A block diagram of the model is also given. Several illustrative examples are provided to show the efficiency of the proposed method in this manuscript.

Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices

The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamics, a number of the numerical techniques have been developed to obtain the spectrum of Lyapunov exponents for the complex temporal behavior of the systems with a few degree of freedom. Unfortunately, these methods cannot be applied directly to analysis of complex spatio-temporal dynamics of plasma devices which are characterized by the infinite phase space, since they are the spatially extended active media. In the present paper, we propose the method for the calculation of the spectrum of the spatial Lyapunov exponents (SLEs) for the spatially extended beam-plasma systems. The calculation technique is applied to the analysis of chaotic spatio-temporal oscillations in three different beam-plasma model: (1) simple plasma Pierce diode, (2) coupled Pierce diodes, and (3) electron-wave system with backward electromagnetic wave. We find an excellent agreement between the system dynamics and the behavior of the spectrum of the spatial Lyapunov exponents. Along with the proposed method, the possible problems of SLEs calculation are also discussed. It is shown that for the wide class of the spatially extended systems, the set of quantities included in the system state for SLEs calculation can be reduced using the appropriate feature of the plasma systems.

Прогнозирование энергоинвестиционной привлекательности субъектов УрФО

This paper studies the problem of safe and sustainable progressive socio-economic and energy development of Russian regions in terms of reforming economy. In this study, the fractal approach in the framework of nonlinear dynamics for a number of indicators was used, as well as a technique of analysis and behavior forecasting of time series of economic systems at the regional level. The authors have performed forecasting works on energy-investment attractiveness of the subjects of the Ural region up to 2020. The calculations were performed for three scenarios of socio-economic development of regions, which will allow prioritizing the regional energy development and suggesting areas of efficient use of financial, material and energy resources.Consideration of the obtained results will allow governmental bodies to pursue a more balanced policy and allow business entities to identify priority solutions on the enhancement of the investment process in the energy of considered regions.

Transient dynamics between displaced fixed points: An alternate nonlinear dynamical framework for olfaction

Significant insights into the dynamics of neuronal populations have been gained in the olfactory system where rich spatio-temporal dynamics is observed during, and following, exposure to odours. It is now widely accepted that odour identity is represented in terms of stimulus-specific rate patterning observed in the cells of the antennal lobe (AL). Here we describe a nonlinear dynamical framework inspired by recent experimental findings which provides a compelling account of both the origin and the function of these dynamics. We start by analytically reducing a biologically plausible conductance based model of the AL to a quantitatively equivalent rate model and construct conditions such that the rate dynamics are well described by a single globally stable fixed point (FP). We then describe the AL's response to an odour stimulus as rich transient trajectories between this stable baseline state (the single FP in absence of odour stimulation) and the odour-specific position of the single FP during odour stimulation.We show how this framework can account for three phenomena that are observed experimentally. First, for an inhibitory period often observed immediately after an odour stimulus is removed. Second, for the qualitative differences between the dynamics in the presence and the absence of odour. Lastly, we show how it can account for the invariance of a representation of odour identity to both the duration and intensity of an odour stimulus. We compare and contrast this framework with the currently prevalent nonlinear dynamical framework of ‘winnerless competition’ which describes AL dynamics in terms of heteroclinic orbits.This article is part of a Special Issue entitled “Neural Coding”.

Transient dynamics between displaced fixed points: an alternate nonlinear dynamical framework for olfaction

Significant insights into the dynamics of neuronal populations have been gained in the olfactory system where rich spatio-temporal dynamics is observed during, and following, exposure to odours. It is now widely accepted that odour identity is represented in terms of stimulus-specific rate patterning observed in the cells of the antennal lobe (AL). Here we describe a nonlinear dynamical framework inspired by recent experimental findings which provides a compelling account of both the origin and the function of these dynamics. We start by analytically reducing a biologically plausible conductance based model of the AL to a quantitatively equivalent rate model and construct conditions such that the rate dynamics are well described by a single globally stable fixed point (FP). We then describe the AL's response to an odour stimulus as rich transient trajectories between this stable baseline state (the single FP in absence of odour stimulation) and the odour-specific position of the single FP during odour stimulation. We show how this framework can account for three phenomena that are observed experimentally. First, for an inhibitory period often observed immediately after an odour stimulus is removed. Second, for the qualitative differences between the dynamics in the presence and the absence of odour. Lastly, we show how it can account for the invariance of a representation of odour identity to both the duration and intensity of an odour stimulus. We compare and contrast this framework with the currently prevalent nonlinear dynamical framework of 'winnerless competition' which describes AL dynamics in terms of heteroclinic orbits. This article is part of a Special Issue entitled "Neural Coding".

Building interfaces between the humanities and cognitive sciences

I argue that creating interfaces between the humanities and cognitive sciences would be intellectually stimulating for both groups. More specifically for the humanities: they might gain challenging and rewarding avenues of inquiry, attract more funding, and advance their position in the 21st-century universities and among the general public, if they engage in interface projects with cognitive science and other disciplines that seek to improve our understanding of what it means to be human. I discuss a potential research framework of non-linear dynamics for such interfaces, and argue that it alleviates some of the concerns of reductionism and determinism that scholars in the humanities might have in relation to the scientific approach. I also discuss some general examples from the study of human speech of how successful interfaces have been built and might be extended to other areas relevant to the humanities.

Vibratory Regime Classification of Infant Phonation

Infant phonation is highly variable in many respects, including the basic vibratory patterns by which the vocal tissues create acoustic signals. Previous studies have identified the regular occurrence of nonmodal phonation types in normal infant phonation. The glottis is like many oscillating systems that, because of nonlinear relationships among the elements, may vibrate in ways representing the deterministic patterns classified theoretically within the mathematical framework of nonlinear dynamics. The infant's preverbal vocal explorations present such a variety of phonations that it may be possible to find effectively all the classes of vibration predicted by nonlinear dynamic theory. The current report defines acoustic criteria for an important subset of such vibratory regimes, and demonstrates that analysts can be trained to reliably use these criteria for a classification that includes all instances of infant phonation in the recorded corpora. The method is thus internally comprehensive in the sense that all phonations are classified, but it is not exhaustive in the sense that all vocal qualities are thereby represented. Using the methods thus developed, this study also demonstrates that the distributions of these phonation types vary significantly across sessions of recording in the first year of life, suggesting developmental changes. The method of regime classification is thus capable of tracking changes that may be indicative of maturation of the mechanism, the learning of categories of phonatory control, and the possibly varying use of vocalizations across social contexts.

Metastability, criticality and phase transitions in brain and its models

This survey of experimental findings and theoretical insights of the past 25 years places the brain firmly into the conceptual framework of nonlinear dynamics, operating at the brink of criticality, which is achieved and maintained by self-organization. It is here the basis for proposing that the application of the twin concepts of scaling and universality of the theory of non-equilibrium phase transitions can serve as an informative approach for elucidating the nature of underlying neural-mechanisms, with emphasis on the dynamics of recursively reentrant activity flow in intracortical and cortico-subcortical neuronal loops.