Chaotic Network Research Articles

Molybdenum mineralization of Serhiivka Au-Mo deposit (Middle Dnipro, Ukrainian Shield)

The article is devoted to molybdenum mineralization of the Eastern flank of Au-Mo Serhiivka deposit, located in the Middle Dnipro megablock of the Ukrainian Shield (USh). The generalized description of mineralization is performed on such important questions: discovery and exploration history, structure and composition of the host rocks, metamorphic and metasomatic alteration of rocks, structural position and localization conditions of molybdenum mineralization, ore composition, description of major ore minerals, morphology of mineralization and the most widespread views about its genesis. Molybdenum ores were discovered and named East-Serhiivka occurrence for the first time in 1974, before the discovery of gold mineralization, which occurred in 1985.
 Serhiivka deposit consists of two Mesoarchaean volcanic-plutonic associations (VPA) of different composition: the early mafic and the late felsic. The Eastern flank of the deposit, where the molybdenum mineralization is concentrated, is a structural knot similar to the lying letter “T”. It is formed by complex joint of the sub-latitudinal Serhiivka and sub-meridional Solone subvolcanic bodies and the East-Serhiivka massif of plagiogranitoids of the late VPA, which intrude basic rocks of early VPA. Molybdenum mineralization is localized in linearly elongated zones with a chaotic network of thin quartz, carbonate-quartz veinlets and poor (2–5 %) sulfide impregnation, including molybdenite. About 20 vein-impregnated ore zones have been recovered with up to 100–150 m thickness and 0,01 to 0,3 %, sometimes more than 1 % average molybdenum grade. The ores are subdivided into two major mineral types: 1) quartz-molybdenite; 2) quartz-sulfide-gold-molybdenite. The main components of ores molybdenite and native gold are associated with pyrite, chalcopyrite, magnetite, occasionally – pyrrhotite, arsenopyrite, scheelite, bismuth telluride, silver and others. Typical non-metallic minerals are quartz, carbonate, feldspar, chlorite, amphibole, biotite, sericite. It is supposed hydrothermal-metamorphogenic genesis of molybdenum (and gold) ores. Molybdenite and gold are rarely detected in the same intersections, which indicates separate genesis of these minerals. According to the accepted classification molybdenum mineralization is systemized as linear stockwork.
 Molybdenum ores of Serhiivka deposit are mostly considered as independent, separate from gold mineralization, potentially workable mine. It is the most prospective one in the Middle Dnipro region, USh and Ukraine in general. We suggest a comprehensive approach to studying, resource and reserves evaluation of Serhiivka deposit, taking into account the potential of both molybdenum and gold mineralization, as well as concentrations of rhenium and osmium in molybdenite. Geological exploration on the base of this approach will increase investment prospects of Serhiivka gold-molybdenum deposit.

Can we detect clusters of chaotic dynamical networks via causation entropy?

It is known that chaotic dynamical systems in the coupled networks can synchronize, and they can even form clusters. Our study addresses the issue of determining the membership information of continuous-time dynamical networks forming clusters. We observe the output vectors of individual systems in the networks and reconstruct the state space according to Takens' embedding theorem. Afterward, we estimate the information-theoretic measures in the reconstructed state space. We propose the average integrated causation entropy as a model-free distinctive measure to distinguish the clusters in the network using the k-means clustering algorithm. We have demonstrated the proposed procedure on three networks that contain Chua systems. The results indicate that we can determine the members of clusters and the membership information from the data, conclusively.

Generating True Random Numbers Based on Multicore CPU Using Race Conditions and Chaotic Maps

A true random number generator (TRNG) is proposed, harvesting entropy from multicore CPUs to generate non-deterministic outputs. The entropy source is the unpredictable sequence of thread access when parallel threads attempt to access the same memory location, known as race condition or data races. Although prior work using the same entropy source exists, they either have low efficiency or insufficient security analysis. The novelty of this work lies in its use of chaotic networks capable of extracting entropy while postprocessing outputs simultaneously. These networks are formulated by coupling chaotic maps in the form of chaotic coupled map lattices which have the capability to amplify minor uncertainties, leading to better performance as compared to other CPU-based TRNGs. We first perform experiments to depict the unpredictable nature of thread access due to race conditions through entropy and scale index analysis. Next, the proposed generator is scrutinized based on a standardized set of evaluation criteria which includes the use of multiple statistical test suites followed by an analysis of its non-deterministic property. We also perform an in-depth entropy analysis of the generator’s outputs and measure its degree of non-periodicity. Results indicate that the proposed chaos-based TRNG is fast, evenly distributed, and is secure enough for applications that have high security requirements.

Management and optimisation of chaotic supply chain system using adaptive sliding mode control algorithm

This paper deals with adaptive super-twisting (STW) sliding mode control (SMC) algorithm to manage chaotic supply chain system. A multi-echelon supply chain system having parametric perturbations and disturbances is presented to demonstrate chaotic nonlinear dynamical behaviours. When changing input variables slightly in the supply chain system, the predicted outputs will be completely different due to chaotic behaviours with bifurcation. In addition, various uncertainties along with exogenous disturbances make the system dynamics more complex to manage as they propagate both upstream and downstream of the supply chain networks. Particularly, the adaptive STW SMC algorithm has been designed for chaos suppression and synchronisation of the supply chain system. Next, the robust control algorithm with adaptive law for the closed-loop system has been proved by using Lyapunov stability theorem. Then, extensive numerical simulations are conducted to demonstrate the validity of the active control synthesis for optimal operations management of chaotic supply chain networks. The control algorithm based on system theory provides satisfactory performance on achieving chaos suppression and synchronisation of the chaotic supply system. The control system theory can be expanded into new integration software applications for operations management of supply chain networks. Finally, the presented control synthesis with dynamical analysis is essential for strategic decision-makers in the modern supply chain management.

Exponential Stabilization of Delayed Chaotic Memristive Neural Networks Via Aperiodically Intermittent Control

This paper investigates the exponential stabilization of delayed chaotic memristive neural networks (MNNs) via aperiodically intermittent control. The issue is proposed for two reasons: (1) The control signal may not always exist in practical applications; (2) How to enlarge the maximum allowable failure interval (MAFI) for sensors is a challenging problem. To surmount these difficulties, an index called the largest proportion of the rest width (LPRW) in the control period is proposed to measure the MAFI in the sense of guaranteeing the closed-loop system performance with the least control cost. Then, by constructing suitable Lyapunov functional in combination with interval matrix method and Halanay inequality, a stabilization criterion is established to determine the relationship between the feedback gain and the LPRW. Meanwhile, an algorithm is proposed to qualitatively analyze the relationship between the feedback gain and the LPRW. In contrast with the previous works, our results can increase the value of LPRW while still maintaining the stability of the closed-loop MNNs. Finally, some comparisons of simulation results demonstrate that the obtained stabilization criterion has some advantages over the existing ones.

Synchronization of chaotic Hopfield networks with time-varying delay: a resilient DOF control approach**This work was supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant Nos. KJ2017A064 and KJ2018ZD007), the Excellent Youth Talent Support Program of Universities in Anhui Province (Grant No. GXYQZD2019021), and the National Natural Science Foundation of China (Grant No. 61503002).

This paper focuses on the issue of resilient dynamic output-feedback (DOF) control for synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delay-dependent criterion for the synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained.

A Multidimensional Hyperjerk Oscillator: Dynamics Analysis, Analogue and Embedded Systems Implementation, and Its Application as a Cryptosystem.

A lightweight image encryption algorithm is presented based on chaos induction via a 5-dimensional hyperjerk oscillator (5DHO) network. First, the dynamics of our 5DHO network is investigated and shown to exhibit up to five coexisting hidden attractors in the state space that depend exclusively on the system’s initial values. Further, a simple implementation of the circuit was used to validate its ability to exhibit chaotic dynamical properties. Second, an Arduino UNO platform is used to confirm the usability of our oscillator in embedded system implementation. Finally, an efficient image encryption application is executed using the proposed chaotic networks based on the use of permutation-substitution sequences. The superior qualities of the proposed strategy are traced to the dynamic set of keys used in the substitution process which heralds the generation of the final ciphered image. Based on the average results obtained from the entropy analysis (7.9976), NPCR values (99.62), UACI tests (33.69) and encryption execution time for 512 × 512 images (0.1141 s), the proposed algorithm is adjudged to be fast and robust to differential and statistical attacks relative to similar approaches.

Design and implementation of a simple dynamical 4-D chaotic circuit with applications in image encryption

We present a simple yet highly dimensional hybrid diode bridge circuit network that can exhibit complex chaotic behaviours. Further, since our network is characterised by smooth fourth-order exponential nonlinearity, we employ a distinctive approach to assess its different properties: we examine the circuit stability near fixed points. Specifically, we evaluate dynamic complexity using the Lyaponov spectrum analysis, bifurcation analysis and phase space trajectories; additionally, we assess coexisting attractors in the parameter space using numerical and experimental analysis. Furthermore, we report assessments of our network in terms of remerging Feigenbaum trees and metastable chaos. Finally, these properties, and especially the chaotic series of the coexisting attractors, were exploited to implement a chaos-based image encryption protocol using S-box construction and PRNG generation mechanisms. To validate the performance of our protocol, we employed standard security analysis including correlation coefficient, pixel change rate, information entropy, time complexity and key space analysis whose outcome were compared alongside available state-of-the-art methods. Outcomes suggest promising applications for our chaotic circuit network in image encryption.

32 Gb/s chaotic optical communications by deep-learning-based chaos synchronization.

Chaotic optical communications were originally proposed to provide high-level physical layer security for optical communications. Limited by the difficulty of chaos synchronization, there has been little experimental demonstration of high-speed chaotic optical communications, and point to multipoint chaotic optical networking is hard to implement. Here, we propose a method to overcome the current limitations. By using a deep-learning-based scheme to learn the complex nonlinear model of the chaotic transmitter, wideband chaos synchronization can be realized in the digital domain. Therefore, the chaotic receiver can be significantly simplified while still guaranteeing security. A successful transmission of 32 Gb/s messages hidden in a wideband chaotic optical carrier was experimentally demonstrated over a 20 km fiber link. We believe the proposed deep-learning-based chaos synchronization method will enable a new direction for further development of high-speed chaotic optical communication systems and networks.

Aging transition in weighted homogeneous and heterogeneous networks

A network consisting of active and inactive dynamical units experiences aging transition as the number of inactive nodes in the network is increased gradually. In this work, we investigate aging transition by exploring the tenacity of network's global oscillation, implemented by considering a weighted network, while the weights are chosen randomly from a uniform distribution. We examine how the critical transition point from oscillatory to non-oscillatory dynamics changes as the width of the distribution is varied. Exact value of the parameter at which the transition occurs is derived analytically, and interestingly it is found to be dependent on the mean weight of the network. Moreover, we observe a correlation between the results for weighted and unweighted cases. The analysis is performed for both Stuart-Landau limit cycle oscillator network and chaotic Hindmarsh-Rose neuronal network organized in the framework of global (homogeneous) and scale-free (heterogeneous) architectures.

The Unpredictability Analysis of Boolean Chaos

To analyze the unpredictability of Boolean chaos, the model for chaotic circuit system based on autonomous Boolean network is established. In addition, the equations of the Boolean network with propagation time jitter are deduced. By considering the jitter of propagation time because of phase noise, the time for the growth of entropy for an ensemble of trajectories is analyzed. It is demonstrated that Boolean chaos will be unpredictable after tens of nanoseconds, and less average time for the growth of entropy is required as the jitter strength increased. It is shown that Boolean chaos has physical randomness because of phase noise and it also lays the theoretical foundation for the entropy source of true random number generator using chaotic Boolean network.

Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi

Kaotik sistemler birbirine durum değişkenleri üzerinden bağlandığında uygun şartlarda öbek eşzamanlılık gerçekleştirebileceği bilinmektedir. Sürekli zamanlı sistemlerden oluşan böyle bir ağda örneklenmiş gözlem vektörleri kullanılarak ağın içindeki öbeklerin belirlenmesi problemi ele alınmıştır. Buna ek olarak; ağ içerisinde bağlantı şiddetinin değişmesi sonucu yeni öbekler oluşursa öbeklerin yeniden belirlenebileceği ön görülmektedir. Öbek eşzamanlılığın belirlenmesi için bilgi kuramı ölçütlerinden biri olan nedensellik entropisi ölçütünün kestirimleri yapılmıştır. Bu ölçüt aynı ya da farklı öbekte olan kaotik sistemleri birbirinden ayrıştırmaktadır.

Cortical reliability amid noise and chaos

Typical responses of cortical neurons to identical sensory stimuli appear highly variable. It has thus been proposed that the cortex primarily uses a rate code. However, other studies have argued for spike-time coding under certain conditions. The potential role of spike-time coding is directly limited by the internally generated variability of cortical circuits, which remains largely unexplored. Here, we quantify this internally generated variability using a biophysical model of rat neocortical microcircuitry with biologically realistic noise sources. We find that stochastic neurotransmitter release is a critical component of internally generated variability, causing rapidly diverging, chaotic recurrent network dynamics. Surprisingly, the same nonlinear recurrent network dynamics can transiently overcome the chaos in response to weak feed-forward thalamocortical inputs, and support reliable spike times with millisecond precision. Our model shows that the noisy and chaotic network dynamics of recurrent cortical microcircuitry are compatible with stimulus-evoked, millisecond spike-time reliability, resolving a long-standing debate.

Chaotic Interval Type-2 Fuzzy Neuro-oscillatory Network (CIT2-FNON) for Worldwide 129 Financial Products Prediction

In this paper, the author proposes an innovative Chaotic Interval Type-2 Fuzzy Neuro-oscillatory Network (CIT2-FNON) for worldwide financial prediction. Inspired by the author’s original work on Lee-oscillator—a chaotic discrete-time neural oscillator with profound transient-chaotic property, CIT2-FNON provides: (1) effective modeling of Interval Type-2 Fuzzy Logic with Chaotic Transient-Fuzzy Membership Function (CTFMF); and (2) time-series recurrent neural network training and prediction with Chaotic Bifurcation Transfer Function (CBTF). Different from the contemporary research on Type-2 Fuzzy Logic Systems (T2FLS) which mainly focus on the RD and (2) different from contemporary fuzzy-neuro systems which focus on the integration of fuzzy logic and neural networks as separated functional modules, the CIT2-FNON introduced in this paper is constructed by Lee-oscillators which serves as “transient-fuzzy input neurons” of the recurrent network and effectively converts it into CT2TFL system. In other words, the chaotic transient-fuzzification process is actually part of the neural model of the CIT2-FNON. From the implementation perspective, CIT2-FNON is integrated with 2048-trading day time-series financial data and Top-10 major financial signals as financial fuzzy signals (FFS) for the real-time prediction of 129 worldwide financial products.

Multi-user image encryption algorithm based on synchronized random bits generator in semiconductor lasers network

A chaos-based public channel image encryption algorithm among three users is proposed, where the random bits (RBs) generated in a star-type chaotic laser network can be well synchronized and are used as the keys. The proposed algorithm is simple and efficient. Firstly, random bits with verified randomness are generated from the synchronized chaotic semiconductor lasers in a star-type network at a rate of 10Gb/s. Next, lower-triangular error-bits detection is employed to delete the different bits among all the parties over the public channel. Based on the synchronized RBs, the XOR operation is used to diffuse the plain image. Then the hash algorithm is used to get the control parameters matrix from the plain image, and 3D cat map is used to confuse the pixel position through the parameters matrix. Finally, the encrypted image is transmitted in the public channel. The performance tests results, such as key sensitivity, histogram, correlation, differential attack, robustness and entropy analysis, show that the suggested algorithm prevents a powerful computational eavesdropper. Besides, the running speed of this algorithm is linear with the size of plain image. These results open possibilities for multi-user secure communication application.

Synchronization of complex networks of identical and nonidentical chaotic systems via model-matching control.

In this work, a synchronization scheme for networks of complex systems is presented. The proposed synchronization scheme uses a control law obtained with some definitions from graph theory and solving the Model-Matching Problem for complex networks. In particular, Rössler, Chen, Lorenz and Lü chaotic systems are used as complex chaotic systems into complex networks. Particular cases with regular and irregular networks of six identical chaotic systems are implemented, with some well-known topologies as star and ring small-world, and tree topologies. Highlighting, the obtained control law is applied to synchronize an irregular network of six different chaotic systems in a tree topology. The usefulness and advantages of the proposed synchronization scheme are highlighted performing numerical simulations of the chaotic complex networks.

Chaotic Type-2 Transient-Fuzzy Deep Neuro-Oscillatory Network (CT2TFDNN) for Worldwide Financial Prediction

Over the years, financial engineering ranging from the study of financial signals to the modeling of financial prediction is one of the most exciting topics for both academia and financial community. With the flourishing AI technology in the past 20 years, various hybrid intelligent financial prediction systems with the integration of neural networks, chaos theory, fuzzy logic, and genetic algorithms have been proposed. An interval type-2 fuzzy logic system (IT2FLS) with its remarkable capability for the modeling of highly uncertain events and attributes provides a perfect tool to interpret various financial phenomena and patterns. In this paper, the author proposes a chaotic type-2 transient-fuzzy deep neuro-oscillatory network with retrograde signaling (CT2TFDNN) for worldwide financial prediction. With the extension of author's original work on Lee oscillator—a chaotic discrete-time neural oscillator with profound transient-chaotic property—CT2TFDNN provides: effective modeling of an IT2FLS with a chaotic transient-fuzzy membership function; and effective time-series network training and prediction using a chaotic deep neuro-oscillatory network with retrograde signaling. CT2TFDNN not only provides a fast chaotic fuzzy-neuro deep learning and forecast solution, but also successfully resolves the massive data overtraining and deadlock problems, which are usually imposed by traditional recurrent neural networks using classical sigmoid-based activation functions. From the implementation perspective, CT2TFDNN is integrated with 2048 trading-day time-series financial data and top-10 major financial signals as fuzzy financial signals for the real-time prediction of 129 worldwide financial products that consists of: nine major cryptocurrencies, 84 worldwide forex, 19 major commodities, and 17 worldwide financial indices.

Necessary Conditions for Complete Synchronization of a Coupled Chaotic Aihara Neuron Network with Electrical Synapses

In this paper, the synchronization problem of a chaotic Aihara neuron network is considered. Based on the master stability function (MSF) analysis, some necessary conditions are proposed to investigate the complete synchronization of the electrical coupled chaotic Aihara neuron networks. Especially, the two-dimensional parameter-space plots are obtained numerically to visualize the possible synchronized region. For the chaotic Rulkov neuron network, the numerical simulations of the MSF show that complete synchronization of the electrical coupled Aihara neuron network can be achieved when the coupling strength lies in a suitable interval, while it is highly improbable to attain complete synchronization when all neurons are in the chaotic bursting. Moreover, the complete synchronization cannot be reached with further increase or decrease of coupling strength. These results are probably common features as far as discrete-time neuron networks are concerned. Finally, based on the drive-response active control method, an LMI-based criterion is obtained to ensure complete synchronization of the available chaotic Aihara neuron network. The spatiotemporal patterns measured by the state distribution of neurons are employed to validate the effectiveness of our control scheme.

Clustering Using Chaotic Circuit Networks with Weighted Couplings

In this paper, we focus on clustering phenomena in a network composed of coupled chaotic circuits. In this investigation, the coupling strength is reflected by the distance information when the chaotic circuits are placed in a two-dimensional grid. We observe various clustering phenomena in the network of coupled chaotic circuits when we vary the scaling parameters, including the coupling strength, the distance between coupled chaotic circuits and the density of the chaotic circuits.

Lysosomal Pathways and Autophagy Distinctively Control Endothelial Cell Behavior to Affect Tumor Vasculature

Cancer cell-stromal cell crosstalk is orchestrated by a plethora of ligand-receptor interactions generating a tumor microenvironment (TME) which favors tumor growth. The high pro-angiogenic nature of the TME perpetuates the chaotic network of structurally immature, low pericyte-covered vessels characteristic of the tumor vasculature. We previously demonstrated that chloroquine (CQ) -a lysosomotropic agent used as first-generation autophagy blocker in clinical trials- induced tumor vessel normalization and reduced tumor hypoxia. CQ improved both vessel structure and maturation, whereas the conditional knockout of the crucial autophagy gene Atg5 in endothelial cells (ECs) did not, thus highlighting a potential differential role for EC-associated autophagy and the lysosomes in pathological tumor angiogenesis. However, how CQ or ATG5-deficiency in ECs affect angiogenic signals regulating EC-pericyte interface and therefore vessel maturation, remains unknown. Here, we show that in ECs CQ constrained VEGF-A-mediated VEGF receptor (VEGFR)2 phosphorylation, a driver of angiogenic signaling. In the presence of CQ we observed increased expression of the decoy receptor VEGFR1 and of a lower molecular weight form of VEGFR2, suggesting receptor cleavage. Consequently, VEGF-A-driven EC spheroid sprouting was reduced by CQ treatment. Furthermore, CQ significantly affected the transcription and secretion of platelet-derived growth factor (PDGF)-AB/BB (upregulated) and Endothelin-1 (EDN1, downregulated), both modulators of perivascular cell (PC) behavior. In contrast, silencing of ATG5 in ECs had no effect on VEGFR2 to VEGFR1 ratio nor on PDGFB and EDN1 expression. Accordingly, mice harboring B16F10 melanoma tumors treated with CQ, displayed both an increased number of αSMA+ PCs covering tumor vessels and co-expressed PDGF receptor-β, enabling PDGF ligand dependent recruitment. Moreover, upon CQ treatment the tumoral expression of angiopoietin-1 (Angpt1), which retains mural cells, and induces vessel stabilization by binding to the EC-localized cognate receptor (TIE2), was increased thus supporting the vessel normalization function of CQ. These features associated with improved tumor vasculature were not phenocopied by the specific deletion of Atg5 in ECs. In conclusion, this study further unravels endothelial cell autonomous and non-autonomous mechanisms by which CQ “normalizes” the intercellular communication in the tumor vasculature independent of autophagy.