Chaos Model Research Articles

Modulation of Phase-Locking Characteristics of NbOx Memristor by Ag Doping.

Memristors based on niobium oxide have attracted wide interest due to their applications in artificial neural network. Phase-locking (PL) characteristics of NbOx newly explored roots in complex nonlinear dynamics and exhibits great potential in periodical signal handling because of its bioinspired nature. In this study, we fabricate a Pd/Nb/Ag-NbOx/Nb/Pd memristive structure and study the effects of Ag doping on the PL characteristics. We clearly see that the NbOx memristor responds to signal in three distinct patterns. For the low-frequency input, the memristor fires spike series and locks the phase near during the positive period of sinusoidal input, and it encodes the input features by the spike number per period. For the middle-frequency input, the memristor fires one spike per period at a definite phase. The output has the same frequency as the input. The locked phase is proportional to the input frequency. For the high-frequency input, the memristor transforms high frequency to low frequency signal and locks at a definite phase higher than 2π. We combined the microstructural analysis and chaos dynamics to know that Ag doping will lower the activation energy, enhance the responding rate, and enhance thermal conductivity, which extends the locked frequency to 1.7 times the value of the undoped NbOx memristor. We also obtained the locked frequency of even 40 MHz after modulating the elementary circuit configuration according to the material modification and chaos model. Our study proposes to handle a signal with high efficiency resembling auditory sense and inspires a novel artificial intelligent computation prototype.

Solvable Models of Many-Body Chaos from Dual-Koopman Circuits.

Dual-unitary circuits are being vigorously studied as models of many-body quantum chaos that can be solved exactly for correlation functions and time evolution of states. Here we study their classical counterparts defining dual-canonical transformations and associated dual-Koopman operators. Classical many-body systems constructed from these have the property, like their quantum counterparts, that the correlations vanish everywhere except on the light cone, on which they decay with rates governed by a simple contractive map. Providing a large class of such dual-canonical transformations, we study in detail the example of a coupled standard map and show analytically that arbitrarily away from the integrable case, in the thermodynamic limit the system is mixing. We also define "perfect" Koopman operators that lead to the correlation vanishing everywhere including on the light cone and provide an example of a cat-map lattice which would qualify to be a Bernoulli system at the apex of the ergodic hierarchy.

Ergodic theory of diagonal orthogonal covariant quantum channels

We analyse the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic matrix. This allows us to exploit tools from classical ergodic theory to study quantum ergodicity of such channels. As an application of our analysis, we study dual unitary brickwork circuits which have recently been proposed as minimal models of quantum chaos in many-body systems. Upon imposing a local diagonal orthogonal invariance symmetry on these circuits, the long-term behaviour of spatio-temporal correlations between local observables in such circuits is completely determined by the ergodic properties of a channel that is covariant under diagonal orthogonal transformations. We utilize this fact to show that such symmetric dual unitary circuits exhibit a rich variety of ergodic behaviours, thus emphasizing their importance.

Projected state ensemble of a generic model of many-body quantum chaos

Abstract The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times t k = O ( log ⁡ k ) . Our results are supported with numerical simulations performed at q = 2.

Image encryption hiding algorithm based on digital time-varying delay chaos model and compression sensing technique

Most of the existing image encryption algorithms encrypt images as meaningless cryptographic images, which can easily attract the attention of attackers during transmission. To address this problem, scholars have proposed to hide the cipher image in a meaningless carrier image. However, larger carrier images are often required, which occupy more bandwidth. In order to solve this problem, this paper realizes embedding the color secret image into the carrier image whose size is equal to or even smaller than the original image by combining the chaotic compressed sensing model. First of all, the original image is sparsely processed using discrete wavelet transform. Then the time varying delay chaotic model is used to generate pseudo random sequence and then the measurement matrix is constructed to compress and encrypt the image. In the end, using singular value decomposition to achieve image embedding, the carrier image carrying information is obtained.

Dynamical System Analysis of Reference Evapotranspiration using Chaos Models in Some Selected States in Northern Nigeria

Dynamical System Analysis of Reference Evapotranspiration using Chaos Models in Some Selected States in Northern Nigeria

Analysis of Multistability of Financial Risk Chaos Systems and Its Application to Voice Cryptography

In the chaos literature, the application of modeling and control of dynamic systems in chaos theory arising in several fields is investigated. In this article we analyze complex financial chaos systems with countries as interest rates, investment demand, and price indices. The proposed chaotic flow's dynamic behavior is examined using phase portraits, eigenvalues, bifurcation diagrams, and Lyapunov exponent spectra. A significant quantity of research on secure communication systems has been published in recent years as a result of the major advancements in communications equipment and encryption techniques. A new voice encryption algorithm design is given using a financial chaos model. An application for voice encryption is conducted using the suggested algorithm, and the outcomes are described.

High-security space division multiplexing optical transmission scheme based on constellation grid selective twisting

In this paper, we propose a high-security space division multiplexing optical transmission scheme based on constellation grid selective twisting, which adopts the Rossler chaos model for encrypting PDM-16QAM signals, being applied to a multicore, few-mode multiplexing system. The bitstream of the program is passed through XOR function before performing constellation grid selective twisting and rotation of the constellation map to improve the security of the system. The proposed system is verified experimentally by using 80-wave and 4-mode multiplexing in one of the 19-core 4-mode fibers. Based on the proposed encryption method, a net transmission rate of 34.13 Tbit/s, a transmission distance of 6000 km, and a capacity distance product of 204.8 Pb/s × km is achieved under encrypted PDM-QPSK modulation. Likewise, a net transmission rate of 68.27 Tbit/s, a transmission distance of 1000 km, and a capacity distance product of 68.27 Pb/s × km is achieved based on encrypted PDM-16QAM modulation. It is experimentally verified that the sensitivity of the initial value in Rossler's chaotic model is in the range of 10−16∼10−17. Meanwhile, the proposed encryption scheme achieves a large key space of 10101, which is compatible with the high-capacity distance product multicore and few-mode multiplexing system. It is a promising candidate for the next-generation highly-secured high-capacity transmission system.

Short message encryption technology of Beidou communication based on SM9

AbstractTo reduce the security authentication time cost, forwarding delay, and enhance message security of Beidou communication short messages, this paper proposes a Beidou communication short message encryption technology based on SM9 (Mobile Code Secure Communication). This technology uses split hierarchical clustering algorithm to cluster the short message data of Beidou Communication, in order to unify the processing of similar short message data and improve the encryption efficiency of subsequent short messages. Based on the data clustering results, this paper constructs a short message forwarding verification model using the SM9 identification password algorithm, and provides the message content of the communication application protocol and the communication receiving information protocol to achieve low‐cost and efficient forwarding verification. In addition, this article improves the initial value selection of Logistic chaotic mapping by coupling the tent map with coupled mapping lattice (CML) in the spatiotemporal chaos model to generate a chaotic initial value sequence, thereby expanding the key space, enhancing the ability to resist exhaustive attacks, enhancing the randomness of the generated key parameters, and optimizing the encryption effect of short messages. The experimental results show that the short message security authentication time of the technology proposed in this article is basically controlled within 25 ms, and the minimum forwarding delay is only 23.9 ms, which can effectively resist attacks and improve the security of Beidou communication.

KINETIC MODELS OF CHAOS IN LINEAR CATALYTIC REACTIONS

Chaos (chaotic oscillations, strange attractors) are aperiodic changes in certain parameters of the dynamic system under study, which differ from other types of oscillations (damped, undamped, multi-periodic) by unusually complex, unpredictable dynamic behavior, and can be observed for an arbitrarily long time. From the theory of dynamical systems it follows that chaotic oscillations can be described by nonlinear systems of ordinary differential equations with three or more independent variables. Until now, such differential equations have been used to construct kinetic models within the framework of the ideal law of mass action, describing chaotic oscillations in homogeneous and heterogeneous catalytic reactions. Moreover, these kinetic models describe chaotic oscillations only for reactions occurring according to stage schemes that are nonlinear with respect to intermediate substances. This article explores the possibility of describing chaotic oscillations by linear systems of ordinary differential equations with three independent variables, which, within the framework of the nonideal Marcelin-de Donde kinetic law, correspond to stage schemes linear in intermediate substances. It is shown that in real conditions, when the Marcelin-de Donde law is satisfied, kinetic models of mechanisms linear in intermediate substances make it possible to describe any complex dynamic behavior of catalytic reactions. Four-stage linear schemes in intermediate substances have been established, the kinetic models of which describe chaotic oscillations of the reactions of interaction between nitrogen monoxides and carbon monoxides (2NO + CO → N2O + CO2) and the oxidation of carbon monoxide (2CO + O2 → 2CO2) on platinum catalysts with Marcelin-de Donde kinetics in an isothermal gradientless reactor. For citation: Kol'tsov N.I. Kinetic models of chaos in linear catalytic reactions. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2024. V. 67. N 5. P. 121-127. DOI: 10.6060/ivkkt.20246705.6956.

Cosmic ray particles propagation in the Earth’s magnetic field defined with IGRF and CHAOS models

We simulated the galactic cosmic rays’ particles propagation in the Earth’s magnetosphere, given by the IGRF and CHAOS magnetic field models, while the second of them additionally has a lithospheric field component that is absent in the first model. The power spectra of the flux of galactic cosmic rays at a fixed height above the Earth’s surface are obtained and their difference is found for large orders of the multipole expansion, l 7. For l 20, the result can be explained by the contribution of the lithospheric component of the magnetic field in the CHAOS model compared to IGRF, and for l 20, the difference in the accuracy of the description of the main field, since IGRF is limited to the 13th order of expansion.

Propagation of Cosmic Ray Particles in the Earth’s Magnetic Field, as Defined by the IGRF and CHAOS Models

Propagation of Cosmic Ray Particles in the Earth’s Magnetic Field, as Defined by the IGRF and CHAOS Models

Early detection of thermoacoustic instability in an O2/CH4 single-injector rocket combustor using analysis of chaos and deep learning models

Thermoacoustic instability (TAI) presents a critical challenge for lean-burning combustors and rocket engines. The early detection of instability is crucial, and to address this, a data-driven prediction framework has been established for TAI in a sub-scale rocket combustor with variable chamber length. Nonlinear combustion features are generated from time series of dynamic pressure using recurrence matrices. Deep learning models are then utilized to train these features and predict the proximity of impending TAI. The performance of the proposed method is investigated through cross-validations of 12 groups of hot-fire test datasets. Remarkably, the prediction performances are in good agreement with measured experimental data, with most instabilities being predicted dozens of milliseconds in advance. This capability paves the way for the early implementation of active control systems in full-scale combustors in the future. The prediction performances are also compared with state-of-the-art TAI prediction methods.

Dual symplectic classical circuits: An exactly solvable model of many-body chaos

We propose a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of symplectic dynamics in two orthogonal (time and space) directions. In close analogy with quantum dual-unitary circuits, we prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. The dynamical correlations are exactly computable in terms of a one-site Markov transfer operator, which is generally of infinite dimensionality. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain. Remarkably, expressing these models in the form of a composition of rotations leads to a transfer operator with a block diagonal form in the basis of spherical harmonics. This allows us to obtain analytical predictions for simple local observables. We demonstrate the validity of our theory by comparison with Monte Carlo simulations, displaying excellent agreement with the latter for a choice of observables.

Maximum entropy model of chaotic explosion and implosion of a large gas bubble in liquid

A mathematical model for the chaotic explosion of a large gas bubble in a liquid is presented in which there is a maximum increase in entropy. It is shown that this requires that the acoustic radiation during the chaos must be minimal and that the spherical surface at the end of the chaos must be stable. Also, a model including the acoustic radiation is developed for the spherical phases of the explosion and implosion of the bubble during which there is no change in entropy. The (final) chaotic phase of the implosion is also modeled so that there is a maximum increase in entropy. There might be additional periods of the bubble during which the bubble explodes and implodes in a similar fashion as the first period. The calculations using this model are shown to agree reasonably well with the data. In particular, these calculations determined that the ratio of the duration of the second period of the bubble to the first period imply that the energy lost in the first period during its implosion is about 2/3 of the energy of the first period. Also, these calculations determine that only about 30% of the total energy is radiated and the rest is absorbed by the water for a total of about 2/3 of the total energy. This also agrees with the data. Furthermore, the data appear to scale with initial total energy as in the calculations using this chaos model.

Mutil-medical image encryption by a new spatiotemporal chaos model and DNA new computing for information security

Mutil-medical image encryption by a new spatiotemporal chaos model and DNA new computing for information security

Ergodicity Breaking and Self-Destruction of Cancer Cells by Induced Genome Chaos.

During the progression of some cancer cells, the degree of genome instability may increase, leading to genome chaos in populations of malignant cells. While normally chaos is associated with ergodicity, i.e., the state when the time averages of relevant parameters are equal to their phase space averages, the situation with cancer propagation is more complex. Chromothripsis, a catastrophic massive genomic rearrangement, is observed in many types of cancer, leading to increased mutation rates. We present an entropic model of genome chaos and ergodicity and experimental evidence that increasing the degree of chaos beyond the non-ergodic threshold may lead to the self-destruction of some tumor cells. We study time and population averages of chromothripsis frequency in cloned rhabdomyosarcomas from rat stem cells. Clones with frequency above 10% result in cell apoptosis, possibly due to mutations in the BCL2 gene. Potentially, this can be used for suppressing cancer cells by shifting them into a non-ergodic proliferation regime.

Application of two-dimensional chaotic system and implementation of DSP

Abstract Given that the limited complexity of most current 2D maps undermines chaos-based practical applications, this paper proposes a 2D Logical Cosine Coupled Map (2D-LSCCM) and compares the bifurcation maps, Lyapunov exponent spectrum, and spectral entropy complexity of the classical 2D chaos model. Based on this model, this paper proposes an image encryption scheme using ascending alignment permutation and XOR pixel diffusion algorithm. After a series of tests, such as chi-square test, anti-attack test, key sensitivity test, and correlation test, the simulation findings show that the chaotic system proposed in this paper has excellent security performance compared with other systems. Moreover, a hardware platform based on DSP (Digital Signal Processing) and NIST test have been developed to analyze and test chaotic sequences.

Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model.

We point out that a classical analog of the Sachdev-Ye-Kitaev (SYK) model, a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equationin the turbulent regime and the nonlinear Schrödinger equationdescribing plasma turbulence, in which there is mixing between many different modes, the random coupling model has a Gaussian-random coupling between any four of a large number N of modes. The model was solved in the 1960s, before the introduction of large-N path-integral techniques, using a method referred to as the direct interaction approximation. We use the path integral to derive the effective action for the model. The large-N saddle gives an integral equationfor the two-point function, which is very similar to the corresponding equationin the SYK model. The connection between the SYK model and the random coupling model may, on the one hand, provide new physical contexts in which to realize the SYK model and, on the other hand, suggest new models of turbulence and techniques for studying them.

High-security three-dimensional optical transmission mechanism utilizing time-frequency-space interleaving disruption.

In this paper, we propose a high-security three-dimensional optical transmission system utilizing time-frequency-space interleaving chaos, which simultaneously enhances the reliability and security of the system. The four-wing 3D chaos model encrypts the time-frequency space interleaved modulation domain of a orthogonal time-frequency space (OTFS) modulation signal and the modulated phase information simultaneously, improving the system's security. We also experimentally validate the proposed high-security 3D-OTFS method, utilizing the hexadecimal modulation technique. The modulated OTFS signal achieves a transmission rate of 34.1 Gb/s over a 2-km seven-core fiber link, with the OTFS signal exhibiting a maximum of 1.31 dB receiver sensitivity gain compared to orthogonal frequency division multiplexing (OFDM) signals under the forward error correction threshold of the bit error rate. The achieved keyspace is equal to 5 × 1048. The findings demonstrate that the proposed high-security three-dimensional optical transmission mechanism, based on time-frequency-space interleaved disruption, exhibits excellent anti-interference ability and confidentiality performance. Consequently, it holds promising prospects for future applications in optical communications.