Nonlinear Transition Research Articles

Bayesian inference for unit root in smooth transition autoregressive models and its application to OECD countries

Abstract This paper proposes a Bayesian unit root test for testing a non-stationary random walk of nonlinear exponential smooth transition autoregressive process. It investigates the performance of Bayes estimators and Bayesian unit root test due to its superiority in estimation and power properties than reported in existing literature. The proposed approach is applied to the real effective exchange rates of 10 selected countries of the organization of economic co-operation and development (OECD) and the paper observe some interesting findings which demonstrate the usefulness of the model.

Quantifying the increase in fishing efficiency due to the use of drifting FADs equipped with echosounders in tropical tuna purse seine fisheries

Abstract Numerous pelagic species are known to associate with floating objects (FOBs), including tropical tunas. Purse seiners use this behaviour to facilitate the capture of tropical tunas by deploying artificial drifting fish aggregating devices (dFADs). One major recent change has been the integration of echosounders in satellite-tracked GPS buoys attached to FOBs, allowing fishers to remotely estimate fishable biomass. Understanding the effects of this new technology on catch of the three main tuna species (yellowfin tuna, Thunnus albacares; bigeye tuna, Thunnus obesus; and skipjack tuna, Katsuwonus pelamis) is important to accurately correct for this change in catch-per-unit-effort (CPUE) indices used for stock assessments. We analysed catch data from the French purse seine fleet for the period 2010–2017 in the Indian Ocean to assess the impact of this fleet’s switch to echosounder buoys around 2012. Results indicate that echosounders do not increase the probability a set will be succesful, but they have a positive effect on catch per set, with catches on average increasing by ≈2−2.5 tonnes per set (≈10%) when made on the vessel's own dFADs equipped with an echosounder buoy. Increases were due to a decrease in sets below ≈25 tonnes and an increase in those greater than ≈25 tonnes, with a non-linear transition around this threshold. This increase explains the considerable investment of purse seiners in echosounder buoys, but also raises concerns about bias in stock size estimates based on CPUE if we do not correct for this fishing efficiency increase.

Cyclicality of Capital Adequacy Ratios in Heterogeneous Environment: a Non-linear Panel Smooth Transition Regression Explanation

This study aims to investigate the cyclicality of capital adequacy ratios (CARs) in US bank holding companies using a new business cycle index and a non-linear panel smooth transition regression model. The suggested index can predict US business activity with a higher accuracy than existing proxies, while the regression methodology deals with the heterogeneity bias of linear models and can capture asymmetric effects, thus improving forecasting efficiency. Our results show that the equity capital to assets ratio is countercyclical, while the risk-based capital adequacy ratios are procyclical. In addition, the response of capital adequacy ratios to changes in economic activity is asymmetric across recessions and expansions. The findings of this study can assist policymakers and bank regulators as the estimation of capital adequacy ratios using the non-linear method and new proxy of BC can improve both the time-lag and accuracy issues in the regulators’ decision making and results in improved compliance behavior of the banks.

Intricate evolutions of multiple-period post-buckling patterns in bilayers

Surface instability of compliant film/substrate bilayers has raised considerable interests due to its broad applications such as wrinkle-driven surface renewal and antifouling, shape-morphing for camouflaging skins, and micro/nano-scale surface patterning control. However, it is still a challenge to precisely predict and continuously trace secondary bifurcation transitions in the nonlinear post-buckling region. Here, we develop lattice models to precisely capture the nonlinear morphology evolution with multiple mode transitions that occur in the film/substrate systems. Based on our models, we reveal an intricate post-buckling phenomenon involving successive flat-wrinkle-doubling-quadrupling-fold bifurcations. Pre-stretch and pre-compression of the substrate, as well as bilayer modulus ratio, can alter surface morphology of film/substrate bilayers. With high substrate pre-tension, hierarchical wrinkles emerge in the bilayer with a low modulus ratio, while a wrinkle-to-ridge transition occurs with a high modulus ratio. Besides, with moderate substrate pre-compression, the bilayer eventually evolves into a period-tripling mode. Phase diagrams based on neo-Hookean and Arruda-Boyce constitutions are drawn to characterize the influences of different factors and to provide an overall view of ultimate pattern formation. Fundamental understanding and quantitative prediction of the nonlinear morphological transitions of soft bilayer materials hold potential for multifunctional surface regulation.

Nonlinear compressive deformations of buckled 3D ribbon mesostructures

Three-dimensional (3D) mesostructures with complex ribbon geometries have widespread applications in a diversified range of areas. The mechanically-guided 3D assembly approach based on precisely controlled buckling provides a versatile route to complex 3D ribbon-shaped mesostructures in a broad set of high-performance materials, thereby allowing the development of 3D flexible electronic devices with new functionalities. In many scenarios of practical operations, especially the biointegrated applications, the 3D flexible electronics would inevitably experience the out-of-plane compression, due to loadings of surrounding bones/organs or clothes, which could affect device functions significantly. A clear understanding of the deformation mode of 3D ribbon-shaped mesostructures is thereby essential to the design of 3D flexible electronics. This paper presents a systematic investigation of nonlinear compressive deformations and mode transitions of bridge-shaped and helical mesostructures assembled through controlled lateral buckling. Based on the elastica theory, a finite-deformation model is developed for the bridge-shaped mesostructure compressed by a frictional wall. Validated by results of experiments and finite element analyses (FEA), this theoretical model enables the establishment of the phase diagram of all possible deformation modes, indicating the crucial roles of friction coefficient and in-plane compressive strain on the mode transition. Experimental and computational studies further show that five distinct deformation modes could possibly occur during the compression of helical mesostructures. The mode transitions in the compressed helical mesostructures are found to arise mainly from the downward collapse, either at the middle or the side region of the mesostructure. These results can serve as design guidelines for the development of 3D flexible electronic devices, especially those for biointegrated applications.

High-dimensional nonlinear wave transitions and their mechanisms.

In this paper, the dynamics of transformed nonlinear waves in the (2+1)-dimensional Ito equation are studied by virtue of the analysis of characteristic line and phase shift. First, the N-soliton solution is obtained via the Hirota bilinear method, from which the breath-wave solution is derived by changing values of wave numbers into complex forms. Then, the transition condition for the breath waves is obtained analytically. We show that the breath waves can be transformed into various nonlinear wave structures including the multi-peak soliton, M-shaped soliton, quasi-anti-dark soliton, three types of quasi-periodic waves, and W-shaped soliton. The correspondence of the phase diagram for such nonlinear waves on the wave number plane is presented. The gradient property of the transformed solution is discussed through the wave number ratio. We study the mechanism of wave formation by analyzing the nonlinear superposition between a solitary wave component and a periodic wave component with different phases. The locality and oscillation of transformed waves can also be explained by the superposition mechanism. Furthermore, the time-varying characteristics of high-dimensional transformed waves are investigated by analyzing the geometric properties (angle and distance) of two characteristic lines of waves, which do not exist in (1+1)-dimensional systems. Based on the high-order breath-wave solutions, the interactions between those transformed nonlinear waves are investigated, such as the completely elastic mode, semi-elastic mode, inelastic mode, and collision-free mode. We reveal that the diversity of transformed waves, time-varying property, and shape-changed collision mainly appear as a result of the difference of phase shifts of the solitary wave and periodic wave components. Such phase shifts come from the time evolution as well as the collisions. Finally, the dynamics of the double shape-changed collisions are presented.

Експериментальні дослідження процесу виявлення нелінійних переходів вибухових пристроїв з неконтактними датчиками цілі

Кардинальні зміни характеру та значне збільшення динаміки ведення мінної війни у воєнних конфліктах сучасності стали результатом зміщення пріоритетів у бік застосування новітніх зразків мінної зброї та саморобних вибухових пристроїв переважно з неконтактними датчиками цілі. Такий стан питання викликав загострення проблеми протидії вибухонебезпечним загрозам, а поряд з цим потребу у забезпеченні потрібного рівня ефективності, безпеки та собівартості процесів пошуку і виявлення вибухових пристроїв з неконтактними (електронними) датчиками цілі. Існуючі технічні засоби пошуку та виявлення вибухонебезпечних предметів, як правило, у більшості випадків ґрунтуються на використанні активних електромагнітних методів. Наближення таких пошукових пристроїв до вибухових пристроїв із магнітними (неконтактними) датчиками цілі або тих, що керуються по радіо, досить часто призводить до несанкціонованого вибуху і як наслідок до втрат.
 Встановлено, що майже усі неконтактні датчики цілі поєднує спільна ознака – наявність напівпровідникових елементів у їхньому складі, або переходів типу метал-окисел-метал. Вказана особливість покладена в основу сучасних засобів виявлення вибухових пристроїв з неконтактними датчиками цілі методом нелінійної радіолокації. Однак, при цьому проблемними досі залишаються вимоги щодо безпеки використання пошукових пристроїв даного типу у ручному варіанті або на наземних транспортних засобах. Одним із шляхів розв’язання даного протиріччя є встановлення пошукових пристроїв на дистанційно-керовану платформу. При чому, виникає нагальна потреба обґрунтування тактико-технічних вимог до засобів даного типу при зміні умов та способів їх застосування.
 На основі проведеного аналізу попередніх досліджень, як вітчизняних, так і закордонних фахівців, стосовно використання електромагнітних методів пошуку і виявлення рукотворних предметів в укриваючих середовищах (ґрунт, сніг, вода тощо), запропоновано науково-методичний підхід щодо планування експериментальних досліджень процесу виявлення нелінійних переходів вибухових пристроїв з неконтактними датчиками цілі. Експериментальні дослідження, призначені для перевірки і уточнення розроблених теоретичних положень щодо створення перспективних дистанційно керованих радіолокаційних комплексів пошуку та виявлення вибухових пристроїв з неконтактними датчиками цілі за допомогою методу нелінійної радіолокації, а у випадку їх підтвердження – технічного обґрунтування вимог до пошукових пристроїв нелінійної радіолокації та дистанційно керованих радіолокаційних комплексів в цілому.

Polarization-selected nonlinearity transition in gold dolmens coupled to an epsilon-near-zero material

Abstract Nonlinear optical materials are cornerstones of modern optics including ultrafast lasers, optical computing, and harmonic generation. The nonlinear coefficients of optical materials suffer from limitations in strength and bandwidth. Also, the nonlinear performance is typically monotonous without polarization selectivity, and to date, no natural material has been found to possess nonlinear coefficients with positive or negative signs simultaneously at a specific wavelength, all of which impede practical applications in the specific scenario. Here, we realize broadband large optical nonlinearity accompanied with ultrafast dynamics in a coupled system composed of gold dolmens and an epsilon-near-zero material for dual orthogonal polarizations simultaneously. The system also shows the polarization-selected nonlinearity transition properties, where the sign of the optical nonlinear refractive indexes can be converted via polarization switching. This guarantees active transitions from self-focusing to self-defocusing by polarization rotation without tuning wavelength in practical utilizations. The measured nonlinear refractive index and susceptibility demonstrate more than three orders of magnitude enhancement over a 400-nm-bandwidth compared with the constituents, while maintaining the sub-1 ps time response. The realized enhanced, ultrafast response, and the polarization tunability ensure the designed system a promising platform for the development of integrated ultrafast laser sources, all-optical circuits and quantum chips.

On the stochastic response regimes of a tristable viscoelastic isolation system under delayed feedback control

In this paper, a tristable viscoelastic isolation system with stochastic excitation under both displacement and velocity delayed feedback control is considered. Firstly, the theoretical expressions of the mean first-passage time (MFPT) to measure the activated escape between different potential wells are derived. Induced nonlinear transition dynamics due to the noise and time delays are mainly discussed. It is found that the delay-induced behaviours affect the transitions between the equilibrium points of the system, the corresponding phenomenon of the delay-enhanced stability is observed. In this respect, the existence of the maxima of the MFPT1 and the MFPT2 is found in one period. Meanwhile, the MFPT1 and the MFPT2 show the monotonic behaviour with the increase of the noise intensity. Additionally, the stationary probability density of the amplitude and the stationary mean amplitude are derived. The influence regimes of the system parameters on both stationary probability density of the amplitude and the stationary mean amplitude are explored. This paper establishes the relationship between system parameters and dynamical properties of the tristable viscoelastic isolation system. This provides a fundamental guidance for the optimization of the viscoelastic isolation by utilizing the technique of delayed feedback control.

The effect of stochasticity with respect to reinfection and nonlinear transition states for some diseases with relapse

In this paper, we consider a stochastic epidemic model with relapse, reinfection, and a general incidence function. Using stochastic tools, we establish a stochastic threshold and prove the extinction of the disease when its value is equal or less than unity. We also show the persistence in mean of the disease when Moreover, we prove the existence and uniqueness of a stationary distribution. Finally, numerical simulations are presented to show the effectiveness of theoretical results.

Nonlinear transition between PT-symmetric and PT-broken modes in coupled fiber lasers.

We present a systematic analysis of the stationary regimes of nonlinear parity-time (PT) symmetric laser composed of two coupled fiber cavities. We find that power-dependent nonlinear phase shifters broaden regions of existence of both PT-symmetric and PT-broken modes, and can facilitate transitions between modes of different types. We show the existence of non-stationary regimes and demonstrate an ambiguity of the transition process for some of the unstable states. We also identify the presence of higher-order stationary modes, which return to the initial state periodically after a certain number of round-trips.

On the nonlinear relationship between energy use and CO2 emissions within an EKC framework: Evidence from panel smooth transition regression in the MENA region

This paper proposes a new approach for analyzing the dynamic relationships between carbon dioxide (CO2) emissions, energy use, and income for the Middle East and North African (MENA) region. Our study implements a class of regime-switching models, namely a nonlinear panel smooth transition regression (PSTR) framework. Two kinds of estimates for carbon emissions are provided. On the one hand, we measure the impact of energy consumption on CO2 concerning the level of income per capita, as countries with a similar energy usage level would have different levels of energy intensity. On the other hand, we estimate the impact of output growth on emissions concerning energy usage variation, as a higher economic growth does not necessarily mean energy-intensive activities. Our empirical findings support these intuitions as they indicate that pollutant emissions respond nonlinearly to energy consumption and GDP growth. We find an inverted U-shaped pattern for the impact of energy on CO2, in the sense that environmental degradation is declining beyond a given income threshold, which is estimated endogenously within the PSTR model. Also, our results underscore that GDP growth significantly impacts carbon emissions only for higher energy consumption growth.

The Impact of Regulatory Quality on the Nexus between Life Insurance Development and Economic Growth: Evidence from European Developing Countries

The purpose of this study is to explore whether the regulatory quality influences the relation between life insurance development and economic growth by applying a nonlinear panel smooth transition regression (PSTR) model. Using the data from Worldwide Governance Indicators (WGI) to assess the soundness of regulatory quality, this paper finds that the relationship between life insurance development and economic growth is significantly positive in the countries with relatively better regulatory quality. Our findings not only indicate that sound regulatory quality could encourage the growth effect of life insurance sectors but also have far-reaching practical implications for other economies to realize regulatory quality should matter for the development of the economic growth.

The dynamics of stratified horizontal shear flows at low Péclet number

Abstract

How technological emergence, saturation, and rejuvenation are re-shaping the e-commerce landscape and disrupting consumption? A time series analysis

Technological advancements in the ICT sector have enabled the development of online platforms that have drastically transformed the e-commerce landscape. The rise of the sharing economy is a key in point. Academics claim that this change is causing a noticeable shift in consumers’ habits from traditional towards collaborative and sharing activities due to environmental, social, and economic motives. In this article, we test the empirical validity of this hypothesis; namely, we test whether or not the recent change in e-commerce landscape is causing a permanent transition in US consumption over the last two decades by fitting a nonlinear smooth transition regression model to the cycle of US consumption with a constructed exogenous regime-driving variable that captures the various aspects of digital technology. The econometric analysis confirms the existence of a non-permanent regime switch in consumption. In particular, we show that the emergence, saturation, and rejuvenation of digital technology are causing consumption to switch between two stationary regimes. Consumption oscillates smoothly, but frequently, between both regimes in the early period (2000-2006) due to the emergence of new technologies and in the recent period (2017-2019) due to technological rejuvenation. It persists, however, in the mid period (2007-2016) due technological saturation.

A contribution to the empirics of food price behavior: the case of rice price dynamics in Italy

PurposeThe purpose is to detect the nonlinearity wholesale rice price formation process in Italy in the 1995–2017 period.Design/methodology/approachA nonlinear smooth transition autoregressive (STAR)-type dynamics model is used.FindingsWholesale rice prices are significantly affected by variations in the international price of rice as well as variations in Arborio price.Research limitations/implicationsThe limitations include policy recommendations for the production and commercialization of rice in Italy.Practical implicationsUnderstanding rice pricing dynamics and nonlinearity behavior is pivotal for the survival of the entire European and Italian rice supply chain.Originality/valueIn the extant literature, no evidence exists on non-linearity of rice prices in Italy.

Transformed nonlinear waves, state transitions and modulation instability in a three-component AB model for the geophysical flows

In this paper, we investigate a three-component AB model, which characterizes the baroclinic instability processes in the geophysical flows. Via the Darboux transformation, the breather solutions are derived. Then, we study the state transition and find that the breather solutions can be transformed into different kinds of stationary nonlinear waves, including the anti-dark soliton, multi-peak soliton, M-shaped soliton, W-shaped solitons and periodic waves. Moreover, by virtue of the second-order transformed solution, various nonlinear wave complexes are presented. Finally, we unveil the relationship between the modulation instability and state transition and show the existence regions for the transformed waves.

Chaos and period-doubling vibration in superconducting levitation systems

For high-temperature superconducting levitation systems, chaotic vibrations occurred under external disturbance, as shown in previous studies. The electromagnetic characteristic of a high-temperature superconductor (HTSC) plays a crucial role in the dynamic stability of levitated systems. In this article, we numerically investigate the HTSC-PM levitation system in nonlinear motions by the finite element method. We analyzed the displacements, temperature, electromagnetic forces, and magnetic field of the HTSC. The results show that the nonlinear vibration transitions from chaos to period-doubling vibration with the HTSC’s temperature and magnetic field change. Furthermore, we select two states from chaos and period-doubling to analyze the natural frequencies. The results show that the electromagnetic characteristics of the HTSC affect the natural frequency of the system.

Exchange rates in India: current account monetarism in a nonlinear context

Abstract The Indian exchange rate system has evolved from a pegged system to the current managed float. The study examines the presence of a long-run equilibrium in the monthly Indian exchange rate (Rs/USD) using a current account monetary model (or flexible price monetary model) while accounting for different nonlinearities over the period January 1993 to January 2014 (pre-inflation targeting period). The nonlinear adjustment to disequilibria is modelled using a nonlinear error correction model (NLECM). The nonlinear current account monetarism (CAM) model includes nonlinear transformations of long-run dynamics in the ECM to account for different nonlinearities: multiple equilibria (cubic polynomial function), nonlinear mean reversion (rational polynomial function), and smooth and gradual regime switches (exponential smooth transition autoregressive (ESTAR) function). The NLECM-ESTAR model outperforms other alternatives based on model and forecast performance measures, implying the existence of nonlinear mean reversion and smooth transition across different periods of overvaluation and undervaluation of the exchange rate. This implies the presence of asymmetric adjustment to the movements from the long-run equilibrium, but the nature of such transitions is smooth and not abrupt. The paper also establishes the uniqueness of the long-run equilibrium. A comparison to the sticky price monetary model could not be made due to stationary exchange rate disequilibrium.

Deformable Generator Networks: Unsupervised Disentanglement of Appearance and Geometry.

We present a deformable generator model to disentangle the appearance and geometric information for both image and video data in a purely unsupervised manner. The appearance generator network models the information related to appearance, including color, illumination, identity or category, while the geometric generator performs geometric warping, such as rotation and stretching, through generating deformation field which is used to warp the generated appearance to obtain the final image or video sequences. Two generators take independent latent vectors as input to disentangle the appearance and geometric information from image or video sequences. For video data, a nonlinear transition model is introduced to both the appearance and geometric generators to capture the dynamics over time. The proposed scheme is general and can be easily integrated into different generative models. An extensive set of qualitative and quantitative experiments shows that the appearance and geometric information can be well disentangled, and the learned geometric generator can be conveniently transferred to other image datasets that share similar structure regularity to facilitate knowledge transfer tasks.