Chaotic Character Research Articles

Variability of SST through Koopman Modes

Abstract The majority of dynamical systems arising from applications show a chaotic character. This is especially true for climate and weather applications. We present here an application of Koopman operator theory to tropical and global sea surface temperature (SST) that yields an approximation to the continuous spectrum typical of these situations. We also show that the Koopman modes yield a decomposition of the datasets that can be used to categorize the variability. Most relevant modes emerge naturally, and they can be identified easily. A difference with other analysis methods such as empirical orthogonal function (EOF) or Fourier expansion is that the Koopman modes have a dynamical interpretation, thanks to their connection to the Koopman operator, and they are not constrained in their shape by special requirements such as orthogonality (as it is the case for EOF) or pure periodicity (as in the case of Fourier expansions). The pure periodic modes emerge naturally, and they form a subspace that can be interpreted as the limiting subspace for the variability. The stationary states therefore are the scaffolding around which the dynamics takes place. The modes can also be traced to the Niño variability and in the case of the global SST to the Pacific decadal oscillation (PDO). Significance Statement We compute the Koopman modes for the tropical and global SST, demonstrating that significant dynamical modes can be identified also in complex high-dimensional datasets with continuous spectra. The Koopman modes are then used to identify the stationary subspace, namely, the limit subspace for the invariant evolution of the system.

Deep reinforcement learning for stock prediction

Due to its chaotic and high volatility character, as well as many other uncertainties from reality, predicting the price of stock market is always a challenging goal to achieve. Due to those characteristics mentioned above, it could be regarded as a classification problem, and then many methods using different machine learning tools could be well applied to solve the challenging problem. Within these methods, deep neural network is a popular and highly noticed one in recent years. This is mainly because of its unique advantages compared to the more conventional machine learning methods, the highly complex nonlienearity and deep nonlinear topologies, to appropriately describe the complex situations. Later, after adding advantages of reinforcement learning to enable the model of the advantages to improve feature dimensions, the deep reinforcement learning method is well proposed to improve the performance. Deep reinforcement learning is a method to combine the advantages of deep learning and the advantages of reinforcement learning, and this paper will discuss its characters and advantages, and finally talk about its limitations and future development.

Anti-bolshevik Insurgencies in Vohlynia in 1919–1920

The study examines the resistance of the population of Vohlynia against the Bolshevik government from the spring of 1919 to the fall of 1920. The author carried out a heuristic search for documents (archival-criminal cases) opened by the employees of the All-Russian Emergency Commission (Vserossiyskaia odzhdenskaia komisia – VChk, in Russian) in the Sectoral State Archive of the Security Service of Ukraine in Rivne, which reveal the specified topic, systematized and analyzed them. On the basis of the narrative synthesized from archival and criminal cases, the author came to the conclusion that the Cheka’s repressions against the participants of anti-Bolshevik insurgencies had an illegal, brutal, chaotic character, systematically violated elementary human rights, and not only the participants of the anti-Bolshevik uprisings, but also ordinary civilians became their victims. At the same time, the scope and implacability of anti-Soviet demonstrations in Vohlynia in 1919–1920, together with the actions of regular Ukrainian and Polish military units, delayed the establishment of the Bolshevik regime there for twenty years. The discussed topic can become the subject of a separate multi-faceted study on the basis of the considered documentary array originating from the departmental archives of the Ukrainian special services. foto 1. Rivne residents Edmund and Maria Żołądziewski with children.Source: HDA SBU, Rivne, f. 5(R), spr. P-10147. foto 2. Director of the 1st Cavalry Army theatrical group, Yefim Gerasimov.HDA SBU, Rivne, f. 4(R), spr. 559.

Fast Fractional Fourier Transform-Aided Novel Graphical Approach for EEG Alcoholism Detection.

Given its detrimental effect on the brain, alcoholism is a severe disorder that can produce a variety of cognitive, emotional, and behavioral issues. Alcoholism is typically diagnosed using the CAGE assessment approach, which has drawbacks such as being lengthy, prone to mistakes, and biased. To overcome these issues, this paper introduces a novel paradigm for identifying alcoholism by employing electroencephalogram (EEG) signals. The proposed framework is divided into various steps. To begin, interference and artifacts in the EEG data are removed using a multiscale principal component analysis procedure. This cleaning procedure contributes to information quality improvement. Second, an innovative graphical technique based on fast fractional Fourier transform coefficients is devised to visualize the chaotic character and complexities of the EEG signals. This elucidates the properties of regular and alcoholic EEG signals. Third, thirty-four graphical features are extracted to interpret the EEG signals' haphazard behavior and differentiate between regular and alcoholic trends. Fourth, we propose an ensembled feature selection method for obtaining an effective and reliable feature group. Following that, we study many neural network classifiers to choose the optimal classifier for building an efficient framework. The experimental findings show that the suggested method obtains the best classification performance by employing a recurrent neural network (RNN), with 97.5% accuracy, 96.7% sensitivity, and 98.3% specificity for the sixteen selected features. The proposed framework can aid physicians, businesses, and product designers to develop a real-time system.

Road not taken? Inventing, modernizing, and renegotiating the concept of association in 19th-century Socialism

ABSTRACT This paper investigates the intellectual lineage of the concept of association in 19th century European socialism. We trace the crucial debates and subsequent rearticulations of the concept, beginning with Charles Fourier’s reflections and further innovations spawned by his followers, finally discussing Edward Abramowski’s attempts to adjust this concept to the Polish context and create a full blown ideology by using it. Our study reveals certain overarching tendencies in the evolution of the concept of association. First, while its initial formulations were based on criticism of the prevailing free competition and the chaotic character of early capitalism, in the later period the concept came in handy in challenging both state apparatuses and socialists wanting to transform society. Second, later reformulations of the concept allowed us to discern that it was no longer solely an intellectual device coming in handy in thinking about the nucleus of the new society, but rather an umbrella-term for a coherent ideological system and mass social movement.

Нестационарные колебания в системе из двух связанных осцилляторов в условиях кубической нелинейности и кубической связи. Часть 1. Мультирежимный характер колебаний

The task about the excitation of magnetoelastic vibrations in geometry of magnetostriction transducer which contains normal magnetized ferrite plate excited by alternating magnetic field is investigated. It is proposed the model presentation of transducer in the view of two connected oscillators first of its corresponds to magnetic part of structure and the second correspond to elastic its part. The first oscillator is linear and the second is nonlinear. The nonlinearity and connection have cubic character. In dependence from the excitation level it is found five basal regimes of vibrations: №1 – synchronize, №2 – three-multiplication of frequency, №3 – chaos, №4 – gigantic oscillations, №5 – delayed stabilization. In these regimes the time-evolvent of vibrations and its parametric portraits in coordinates displacement – derivative from displacement and also frequency spectra of forced vibrations are investigated. The regimes №1б №2 are stable. The vibrations in this regimes are harmonic and complete determined. The regimes №3-№5 are non-stable. The vibrations in this regimes has chaotic or near to chaotic character. On the level of excitation the stable regimes are separated from non-stable by sharp threshold. By the overcoming of which the vibration amplitude increases by sharp jump over two-three orders. By the excitation on non-stable regimes it is established the application on the main vibrations the attendant vibrations. The frequency of attendant vibrations is higher than excitation frequency on two-three orders. The amplitude of attendant vibrations is smaller than the main vibrations amplitude more then two orders. It is proposed the model of attendant vibrations excitations. On the basis of this model the quantity appreciation of vibrations character in non-stable regimes. The recommendations for future development of investigations are proposed.

Dynamics of changes in the number of relapses of tuberculosis in Republic of Tajikistan

Aim . To study the dynamics of changes in the registration of cases of tuberculosis and the frequency of recurrence of the disease in the Republic of Tajikistan between 2011-2020. Material and methods . The work is based on an analysis of official statistics of TB cases between 2010-2020 (National TB register). Results and discussion . Analysis of official statistics for the last 11 years has shown a steady decline in the number of registered TB cases. Thus, this indicator decreased from 7641 cases in 2010 to 4315 in 2020. A deeper analysis of the structure of registered TB cases shows that this decrease is mainly due to a decrease in the number of new TB cases. The dynamics of detection of relapses and repeated cases of the disease over this period were chaotic: either increased sharply or tended to decrease. It should be noted that the dynamics of the decrease in the number of registered TB cases over the 11 years had a similar trend with the number of cases of TB susceptible to anti-TB drugs, while the dynamics of changes in the number of TB cases with resistance to mycobacterium TB also had a chaotic character. Conclusion . An analysis of official statistics over the past 11 years has shown a steady decline in the number of registered TB cases, which is mainly due to a decrease in the number of new TB cases with preserved sensitivity to anti-TB drugs. An analysis of the dynamics of changes in the number of relapses after successful treatment of TB over the past 11 years showed that relapses of the disease are recorded annually in 4.16% and up to 12.9% of the total number of registered TB cases. There are regional differences in incidence and relapse from TB.

A Review on Audio Encryption Using Chaotic Sequences and Finite Field

Audio data are used in various fields such as education, engineering, mathematics, art, advertisement, military, medicine, scientific research, and many more. This excessive growth of audio data boosts the importance of multimedia data processing tools and digital documentation. This access to multimedia data through the internet has created inappropriate prospects which are hazardous for the confidentiality and integrity of the data. To encounter these threats, the domain of audio data security gains broad attention. A considerable number of algorithms have been established to protect personal information over open networks. Finite fields are well-studied algebraic structures with enormous efficient properties which have applications in the fields of cryptology and coding theory. Here, an existing system uses lossless binary Galois field extension based efficient algorithm for audio data encryption. The architecture hired a special type of curve in the diffusion module which depends on efficient elliptic curve arithmetic operations. So, it generates pseudo-random numbers (PRN) and with slight computational efforts, it produces optimum diffusion in the encrypted multimedia files. The method is compared with the proposed system using a scheme uses Henon chaotic map and 128-bit AES secret key in order to generate the cipher audio data. Henon chaotic map is a two dimensional iterated discrete dynamic system that shows chaotic character on specific values of the constants used. Chaotic maps are very sensitive to the initial parameters, i.e., a slight change in the initial conditions drastically changes the overall output generated by the chaotic system. The investigational outcomes through different analyses and time complexity demonstrated the ability of the techniques to counter various attacks. Furthermore, two schemes are compared and more appropriate to be applied for data security.

Shaking Table Seismic Experimental Investigation of Lightweight Rigid Bodies

This study presents the findings of an extensive shaking table experimental campaign conducted on nine free-standing wooden specimens, aiming at providing insights on the rigid body motion of free-standing objects. The specimens, which differ in slenderness and size, are characterized by impairments in their base surface and most likely in their shapes, which also lead to asymmetric responses. The imperfections of the tested objects are an additional source of uncertainty with respect to the intrinsic chaotic character of the rigid body motion, which is a crucial factor that prevents the reproducibility of the tests and induces discrepancies between specimen responses and those of their ideal models. A contactless measurement strategy is employed to assure unaltered data acquisition. The experimental campaign includes free vibration tests, pulse excitation, and natural ground motions tests; the dynamic responses of the specimens are organized and rearranged, aiming at providing a comprehensive set of data that could be employed for calibrating numerical models accounting for imperfect conditions. The damping properties of the specimens are discussed, providing a novel estimation of the coefficient of restitution based on the free vibration tests. The limits of the ideal simple rigid model are highlighted, and the roles of size factor and aspect ratio are discussed according to the obtained results.

A comparative exploration of the chaotic characteristics of Chinese and international copper futures prices

This study used a C–C method to reconstruct the phase space of copper prices from January 2002 to December 2021, using Chinese and international copper futures price time series as a sample. It demonstrates the differences in the chaotic characteristics of two copper futures prices through recurrence plots and correlation dimensions. Recurrence complex networks have been employed to quantify the spatial structural similarity between the variables and copper prices, and the main factors influencing the structural changes in copper prices have been analysed by a systematic bifurcation mechanism. The results show that the efficiency of the copper futures market has improved gradually. The level of perfection and efficiency of the Chinese copper futures market is lower than that of the international copper futures market, and the predictability of Chinese copper futures prices is even weaker, which means that the investment in Chinese copper futures is riskier than that in the international copper futures market. Compared to other metal futures, such as aluminium and nickel, copper futures are likely to be a lower risk investment. The US dollar index, the federal funds rate and the price of gold are the main factors influencing changes in the spatial structure of copper prices in China, while political risk, crude oil and gold prices are key to shaping the chaotic character of international copper prices. A tipping point in the chaotic state of copper prices could correspond to the onset of a global financial crisis. This study can help policymakers to understand the market laws underlying prices and thus create robust and well-traded markets by controlling the chaotic characteristic structure of copper prices. In addition, the identification of chaotic state thresholds in Chinese and international copper prices can predict the occurrence of unexpected events such as financial crises, which is important to counteract financial market risks.

Dissipative quantum dynamics, phase transitions, and non-Hermitian random matrices

We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in open quantum systems. We establish that the Liouvillian describing the quantum dynamics exhibits distinct spectral features of integrable and chaotic character on the two sides of the critical point. We follow the distribution of the spacings of the complex Liouvillian eigenvalues across the critical point. In the normal and superradiant phases, the distributions are two-dimensional Poisson and that of the Ginibre unitary random matrix ensemble, respectively. Our results are corroborated by computing a recently introduced complex-plane generalization of the consecutive level-spacing ratio distribution. Our approach can be readily adapted for classifying the nature of quantum dynamics across dissipative critical points in other open quantum systems.

A novel 0.2–7 GHz microwave hyperchaotic generator based on Hartley oscillator

In this paper, a miniaturized microwave-band hyperchaotic generator prototype has been designed and realized. By improving the topology of Hartley oscillator, the proposed single-stage common-collector structure oscillator enables us to generate a microwave 0.2–7 GHz smooth spectrum signal with a power around −30 dBm. Using BFP650 SiGe transistor as a non-linear component, the proposed circuit has been implemented and simulated then experimentally approved. Introducing the parasitic capacitors C BC and C BE and using the exponential model to describe the active component non-linearity, a simplified electrical model for the developed circuit has been proposed. To exhibit the deterministic chaotic character of the mentioned circuit, mathematical and schematic implementation results using Matlab and Advanced Design System (ADS) simulations have been presented. The concordance between the two simulation results permits us to adopt the simplified state equation model to describe the circuit behavior. The Lyapunov spectrum exponents representation allowed us to verify the hyperchaotic behavior in the presented generator. Finally, an autonomous simple prototype architecture of the generator using the PTFE (Polytetrafluoroethylene) substrate with ε r = 2.2 has been realized and experimentally validated. The achieved performances made the proposed circuit suitable for various fields of telecommunications.

A phytoplankton-zooplankton-fish model with chaos control: In the presence of fear effect and an additional food.

The interplay of phytoplankton, zooplankton, and fish is one of the most important aspects of the aquatic environment. In this paper, we propose to explore the dynamics of a phytoplankton-zooplankton-fish system, with fear-induced birth rate reduction in the middle predator by the top predator and an additional food source for the top predator fish. Phytoplankton-zooplankton and zooplankton-fish interactions are handled using Holling type IV and II responses, respectively. First, we prove the well-posedness of the system, followed by results related to the existence of possible equilibrium points. Conditions under which a different number of interior equilibria exist are also derived here. We also show this existence numerically by varying the intrinsic growth rate of phytoplankton species, which demonstrates the model's vibrant nature from a mathematical point of view. Furthermore, we performed the local and global stability analysis around the above equilibrium points, and the transversality conditions for the occurrence of Hopf bifurcations and transcritical bifurcations are established. We observe numerically that for low levels of fear, the system behaves chaotically, and as we increase the fear parameter, the solution approaches a stable equilibrium by the route of period-halving. The chaotic behavior of the system at low levels of fear can also be controlled by increasing the quality of additional food. To corroborate our findings, we constructed several phase portraits, time-series graphs, and one- and two-parametric bifurcation diagrams. The computation of the largest Lyapunov exponent and a sketch of Poincaré maps verify the chaotic character of the proposed system. On varying the parametric values, the system exhibits phenomena like multistability and the enrichment paradox, which are the basic qualities of non-linear models. Thus, the current study can also help ecologists to estimate the parameters to study and obtain such important findings related to non-linear PZF systems. Therefore, from a biological and mathematical perspective, the analysis and the corresponding results of this article appear to be rich and interesting.

The current state of the plant nomenclature in crop production on the example of dissertation titles

Aim. The aim of this article is to analyze the current state of plant nomenclature in agricultural practice. Methods. The analysis of literary sources, mathematical analysis. Results. In the titles of 1760 analyzed dissertations for the scientific degrees in agricultural sciences (2000–2019), 90.3% of the plant names are presented in Ukrainian, 5.6% are a combination of Ukrainian and Latin names, and 4.1% are in Latin. In the titles of 680 dissertations for the scientific degrees in biological sciences, the main part is made up of the Latin names of taxa of a generic and species rank and below — 45.2%, names in Ukrainian are 35.1%, and combinations of Ukrainian and Latin names are 19.7%. Despite the fact that the same groups of organisms are studied in both groups agricultural and biological, there are significant differences in the use of names. The scientific style of the Ukrainian language is inherent in the direct word order when the adjective precedes the noun. This is how crop names were coined: miaka pshenytsia (common wheat), tverda pshenytsia (durum wheat), ozyma pshenytsia (winter wheat), yara pshenytsia (spring wheat), tsukrovi buriaky (sugar beet), etc., while in the names of botanical taxa the word order is opposite: pshenytsia miaka (common wheat), pshenytsia tverda (durum wheat), buriak zvychainyi (beet), etc. In the last quarter of the twentieth century, unmotivated inversion occurred in the catalogues of zoned cultivars of agricultural crops, when the word order in the crop names changed to the opposite. In the International Convention for the Protection of Rights of New Varieties of Plants, the term variety is associated with the term taxon, and not agricultural crop. Therefore, the concepts of agricultural crop and botanical taxon that are not identical are confused in the State Register of Plant Varieties of Ukraine. Agrarians have been in a state of ambiguity and uncertainty regarding the proper use of plant names. The attempts to assimilate the agrobiological nomenclature to the botanical one led to an unreasonable replacement of the names of cultons, which acquired a chaotic and mass character. At the beginning of the 20th century, in the vast majority of dissertations in the agricultural field, the spelling of the names of traditional crops corresponded to the scientific style, but gradually it changed and now in most dissertations the reverse word order dominates, mistakenly identifying the crop names with specific names. At the same time, in biological dissertation, the names of both cultons and taxa correspond to the scientific style. Conclusions. The titles of many dissertations for the scientific degrees in Agricultural and Biological Sciences use Ukrainian and Latin names of plants. Latin names are regulated by the ICN, but the Ukrainian ones belong to two unregulated terminological systems. The first botanical system reflects the scientific botanical nomenclature and manages the names of taxon, the second agrobiological system is based on the names of cultons. Generic names and crop names often coincide, while species names and crop names differ in word order. In the verbose crop names, the word order is direct with the adjective precedes the noun, in the species names the word order is reversed, a generic name followed by a specific epithet. The phenomenon of replacing crop names with names inheriting the species names has become rampant over the past twenty years. They destroy the system of agrobiological nomenclature and contradict the scientific standards of the literary Ukrainian language. The identification of this negative phenomenon will allow us to overcome it faster.

Orbit evolution in growing stellar bars: bar-supporting orbits at the vertical ILR region

ABSTRACT We investigate the evolution of orbital shapes at the inner Lindblad resonance region of a rotating 3D bar, the mass of which is growing with time. We evaluate in time-dependent models, during a 5 Gyr period, the importance of orbits with initial conditions known to play a significant role in supporting peanut-like structures in autonomous systems. These orbits are the central family of periodic orbits (x1) and vertical perturbations of it, orbits of its standard 3D bifurcations at the region (x1v1 and x1v2), as well as orbits in their neighbourhood. The knowledge of the regular or chaotic character of these orbits is essential as well, because it allows us to estimate their contribution to the support of a rotating bar and, more importantly, the dynamical mechanisms that make it possible. This is calculated by means of the GALI2 index. We find that orbital patterns existing in the autonomous case, persist for longer times in the more massive bar models, and even more so in a model in which the central spheroid component of our adopted galactic potential becomes rather insignificant. The peanut-supporting orbits that we find, have a regular or, in most cases, a weakly chaotic character. There are cases in which orbits starting close to unstable periodic orbits in an autonomous model behave as regular and support the bar when its mass increases with time. As a rule of thumb for the orbital dynamics of our non-autonomous models at a certain time, can be considered the dynamics of the corresponding frozen systems around that time.

A Stacked GRU-RNN-Based Approach for Predicting Renewable Energy and Electricity Load for Smart Grid Operation

Predictions of renewable energy (RE) generation and electricity load are critical to smart grid operation. However, the prediction task remains challenging due to the intermittent and chaotic character of RE sources, and the diverse user behavior and power consumers. This article presents a novel method for the prediction of RE generation and electricity load using improved stacked gated recurrent unit-recurrent neural network (GRU-RNN) for both univariate and multivariate scenarios. First, multiple sensitive monitoring parameters or historical electricity consumption data are selected according to the correlation analysis to form the input data. Second, a stacked GRU-RNN using a simplified GRU is constructed with improved training algorithm based on AdaGrad and adjustable momentum. The modified GRU-RNN structure and improved training method enhance training efficiency and robustness. Third, the stacked GRU-RNN is used to establish an accurate mapping between the selected variables and RE generation or electricity load due to its self-feedback connections and improved training mechanism. The proposed method is verified by using two experiments: prediction of wind power generation using multiple weather parameters and prediction of electricity load with historical energy consumption data. The experimental results demonstrate that the proposed method outperforms state-of-the-art methods of machine learning or deep learning in achieving an accurate energy prediction for effective smart grid operation.

Experimental chaotic synchronization for coupled double pendula.

10.1063/5.0056530.4In this paper, we experimentally verify the phenomenon of chaotic synchronization in coupled forced oscillators. The study is focused on the model of three double pendula locally connected via springs. Each of the individual oscillators can behave both periodically and chaotically, which depends on the parameters of the external excitation (the shaker). We investigate the relation between the strength of coupling between the upper pendulum bobs and the precision of their synchronization, showing that the system can achieve practical synchronization, within which the nodes preserve their chaotic character. We determine the influence of the pendula parameters and the strength of coupling on the synchronization precision, measuring the differences between the nodes' motion. The results obtained experimentally are confirmed by numerical simulations. We indicate a possible mechanism causing the desynchronization of the system's smaller elements (lower pendula bobs), which involves their motion around the unstable stationary position and possible transient dynamics. The results presented in this paper may be generalized into typical models of pendula and pendula-like coupled systems, exhibiting chaotic dynamics.

Нестационарное запаздывание установления нелинейных колебаний в системе двух связанных осцилляторов. Часть 1. Общие положения. Формирование упрощенной системы.

Нестационарное запаздывание установления нелинейных колебаний в системе двух связанных осцилляторов. Часть 1. Общие положения. Формирование упрощенной системы.

Analysis of Pseudo-Lyapunov Exponents of Solar Convection Using State-of-the-Art Observations.

The solar photosphere and the outer layer of the Sun’s interior are characterized by convective motions, which display a chaotic and turbulent character. In this work, we evaluated the pseudo-Lyapunov exponents of the overshooting convective motions observed on the Sun’s surface by using a method employed in the literature to estimate those exponents, as well as another technique deduced from their definition. We analyzed observations taken with state-of-the-art instruments at ground- and space-based telescopes, and we particularly benefited from the spectro-polarimetric data acquired with the Interferometric Bidimensional Spectrometer, the Crisp Imaging SpectroPolarimeter, and the Helioseismic and Magnetic Imager. Following previous studies in the literature, we computed maps of four quantities which were representative of the physical properties of solar plasma in each observation, and estimated the pseudo-Lyapunov exponents from the residuals between the values of the quantities computed at any point in the map and the mean of values over the whole map. In contrast to previous results reported in the literature, we found that the computed exponents hold negative values, which are typical of a dissipative regime, for all the quantities derived from our observations. The values of the estimated exponents increase with the spatial resolution of the data and are almost unaffected by small concentrations of magnetic field. Finally, we showed that similar results were also achieved by estimating the exponents from residuals between the values at each point in maps derived from observations taken at different times. The latter estimation technique better accounts for the definition of these exponents than the method employed in previous studies.

Studies on rubidium 5S-5d two-photon absorption

ABSTRACT We studied non-resonant two photon absorption (NRTPA) 5S1/2→5D5/2 of hot Rb atom using a laser emitting at 778nm. The decay channel 5D5/2→6P3/2→5S1/2 is monitored to record the blue fluorescence. Two important aspects of blue fluorescence are explored: (i) photon number statistics under counter-propagating beam geometry, (ii) extraction of a workable discriminator signal by using modulation transfer for offset locking. The blue photon statistics histogram closely follows super–Poissonian distribution revealing the partially coherent or chaotic character under the limit of large photon counts. On the other hand modulation amplitude vs. peak height of 1-st derivative signal reveals that too small or too large modulation is detrimental for extracting discriminator signal. Under weak modulation, the offset stabilized laser attains square root of Allan variance σ(τ) ∼ 1.5 × 10−10 at integration time τ>10s. We propose generation of an offset stabilized chaotic blue light source by coupling (i) and (ii).