Two-dimensional memristive hyperchaotic maps with different coupling frames and its hardware implementation.

Continuous-time memristors have been used in numerous chaotic circuit systems. Similarly, the discrete memristor model applied to a discrete map is also worthy of further study. To this end, this paper first proposes a discrete memristor model and analyzes the voltage-current characteristics of the memristor. Also, the discrete memristor is coupled with a one-dimensional (1D) sine chaotic map through different coupling frameworks, and two different two-dimensional (2D) chaotic map models are generated. Due to the presence of linear fixed points, the stability of the 2D memristor-coupled chaotic map depends on the choice of control parameters and initial states. The dynamic behavior of the chaotic map under different coupled map frameworks is investigated by using various analytical methods, and the results show that different coupling frameworks can produce different complex dynamical behaviors for memristor chaotic maps. The dynamic behavior based on parameter control is also investigated. The numerical experimental results show that the change of parameters can not only enrich the dynamic behavior of a chaotic map, but also increase the complexity of the memristor-coupled sine map. In addition, a simple encryption algorithm is designed based on the memristor chaotic map under the new coupling framework, and the performance analysis shows that the algorithm has a strong ability of image encryption. Finally, the numerical results are verified by hardware experiments.

Discrete Memristor and Discrete Memristive Systems.

In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G-L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The "∞"-type hysteresis loop curves are observed when input is the bipolar periodic signal. Meanwhile, numerical analysis results show that the area of hysteresis decreases with the increase of frequency of input signal and the decrease of derivative order. Moreover, the memory effect, characteristics and physical realization of the discrete memristors are discussed, and a discrete memristor with short memory effects is designed. Furthermore, discrete memristive systems are designed by introducing the fractional-order discrete memristor and integer-order discrete memristor to the Sine map. Chaos is found in the systems, and complexity of the systems is controlled by the parameter of the memristor. Finally, FPGA digital circuit implementation is carried out for the integer-order and fractional-order discrete memristor and discrete memristive systems, which shows the potential application value of the discrete memristor in the engineering application field.

Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media.

Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.

Spiral waves in a hybrid discrete excitable media with electromagnetic flux coupling.

Though there are many neuron models based on differential equations, the complexity in realizing them into digital circuits is still a challenge. Hence, many new discrete neuron models have been recently proposed, which can be easily implemented in digital circuits. We consider the well-known FitzHugh-Nagumo model and derive the discrete version of the model considering the sigmoid type of recovery variable and electromagnetic flux coupling. We show the various time series plots confirming the existence of periodic and chaotic bursting as in differential equation type neuron models. Also, we have used the bifurcation plots, Lyapunov exponents, and frequency bifurcations to investigate the dynamics of the proposed discrete neuron model. Different topologies of networks like single, two, and three layers are considered to analyze the wave propagation phenomenon in the network. We introduce the concept of using energy levels of nodes to study the spiral wave existence and compare them with the spatiotemporal snapshots. Interestingly, the energy plots clearly show that when the energy level of nodes is different and distributed, the occurrence of the spiral waves is identified in the network.

A hyperchaotic cycloid map with attractor topology sensitive to system parameters.

We propose herein a novel discrete hyperchaotic map based on the mathematical model of a cycloid, which produces multistability and infinite equilibrium points. Numerical analysis is carried out by means of attractors, bifurcation diagrams, Lyapunov exponents, and spectral entropy complexity. Experimental results show that this cycloid map has rich dynamical characteristics including hyperchaos, various bifurcation types, and high complexity. Furthermore, the attractor topology of this map is extremely sensitive to the parameters of the map. The x--y plane of the attractor produces diverse shapes with the variation of parameters, and both the x--z and y--z planes produce a full map with good ergodicity. Moreover, the cycloid map has good resistance to parameter estimation, and digital signal processing implementation confirms its feasibility in digital circuits, indicating that the cycloid map may be used in potential applications.

A Modified Multivariable Complexity Measure Algorithm and Its Application for Identifying Mental Arithmetic Task.

Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.

Distributed Consensus Tracking Control of Chaotic Multi-Agent Supply Chain Network: A New Fault-Tolerant, Finite-Time, and Chatter-Free Approach.

Over the last years, distributed consensus tracking control has received a lot of attention due to its benefits, such as low operational costs, high resilience, flexible scalability, and so on. However, control methods that do not consider faults in actuators and control agents are impractical in most systems. There is no research in the literature investigating the consensus tracking of supply chain networks subject to disturbances and faults in control input. Motivated by this, the current research studies the fault-tolerant, finite-time, and smooth consensus tracking problems for chaotic multi-agent supply chain networks subject to disturbances, uncertainties, and faults in actuators. The chaotic attractors of a supply chain network are shown, and its corresponding multi-agent system is presented. A new control technique is then proposed, which is suitable for distributed consensus tracking of nonlinear uncertain systems. In the proposed scheme, the effects of faults in control actuators and robustness against unknown time-varying disturbances are taken into account. The proposed technique also uses a finite-time super-twisting algorithm that avoids chattering in the system's response and control input. Lastly, the multi-agent system is considered in the presence of disturbances and actuator faults, and the proposed scheme's excellent performance is displayed through numerical simulations.

SEIR modeling of the COVID-19 and its dynamics.

In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input. Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system. We found that the parameters of the proposed SEIR model are different for different scenarios. Then, the model is employed to show the evolution of the epidemic in Hubei province, which shows that it can be used to forecast COVID-19 epidemic situation. Moreover, by introducing the seasonality and stochastic infection the parameters, nonlinear dynamics including chaos are found in the system. Finally, we discussed the control strategies of the COVID-19 based on the structure and parameters of the proposed model.

Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method.

In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.

Parameter Identification of Fractional-Order Discrete Chaotic Systems.

Research on fractional-order discrete chaotic systems has grown in recent years, and chaos synchronization of such systems is a new topic. To address the deficiencies of the extant chaos synchronization methods for fractional-order discrete chaotic systems, we proposed an improved particle swarm optimization algorithm for the parameter identification. Numerical simulations are carried out for the Hénon map, the Cat map, and their fractional-order form, as well as the fractional-order standard iterated map with hidden attractors. The problem of choosing the most appropriate sample size is discussed, and the parameter identification with noise interference is also considered. The experimental results demonstrate that the proposed algorithm has the best performance among the six existing algorithms and that it is effective even with random noise interference. In addition, using two samples offers the most efficient performance for the fractional-order discrete chaotic system, while the integer-order discrete chaotic system only needs one sample.

Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems.

Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel-Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.

Effect of AlCl3 concentration on nanoparticle removal by coagulation.

In recent years, engineered nanoparticles, as a new group of contaminants emerging in natural water, have been given more attention. In order to understand the behavior of nanoparticles in the conventional water treatment process, three kinds of nanoparticle suspensions, namely multi-walled carbon nanotube-humic acid (MWCNT-HA), multi-walled carbon nanotube-N,N-dimethylformamide (MWCNT-DMF) and nanoTiO2-humic acid (TiO2-HA) were employed to investigate their coagulation removal efficiencies with varying aluminum chloride (AlCl3) concentrations. Results showed that nanoparticle removal rate curves had a reverse "U" shape with increasing concentration of aluminum ion (Al(3+)). More than 90% of nanoparticles could be effectively removed by an appropriate Al(3+) concentration. At higher Al(3+) concentration, nanoparticles would be restabilized. The hydrodynamic particle size of nanoparticles was found to be the crucial factor influencing the effective concentration range (ECR) of Al(3+) for nanoparticle removal. The ECR of Al(3+) followed the order MWCNT-DMF>MWCNT-HA>TiO2-HA, which is the reverse of the nanoparticle size trend. At a given concentration, smaller nanoparticles carry more surface charges, and thus consume more coagulants for neutralization. Therefore, over-saturation occurred at relatively higher Al(3+) concentration and a wider ECR was obtained. The ECR became broader with increasing pH because of the smaller hydrodynamic particle size of nanoparticles at higher pH values. A high ionic strength of NaCl can also widen the ECR due to its strong potential to compress the electric double layer. It was concluded that it is important to adjust the dose of Al(3+) in the ECR for nanoparticle removal in water treatment.

Integrated Circuit of a Chua's System Based on the Integral-Differential Nonlinear Resistance with Multi-Path Voltage-Controlled Oscillator.

In this paper, we present a fully integrated circuit without inductance implementing Chua's chaotic system. The circuit described in this study utilizes the SMIC 180 nm CMOS process and incorporates a multi-path voltage-controlled oscillator (VCO). The integral-differential nonlinear resistance is utilized as a variable impedance component in the circuit, constructed using discrete devices from a microelectronics standpoint. Meanwhile, the utilization of a multi-path voltage-controlled oscillator ensures the provision of an adequate oscillation frequency and a stable waveform for the chaotic circuit. The analysis focuses on the intricate and dynamic behaviors exhibited by the chaotic microelectronic circuit. The experimental findings indicate that the oscillation frequency of the VCO can be adjusted within a range of 198 MHz to 320 MHz by manipulating the applied voltage from 0 V to 1.8 V. The circuit operates within a 1.8 V environment, and exhibits power consumption, gain-bandwidth product (GBW), area, and Lyapunov exponent values of 1.0782 mW, 4.43 GHz, 0.0165 mm2, and 0.6435∼1.0012, respectively. The aforementioned circuit design demonstrates the ability to generate chaotic behavior while also possessing the benefits of low power consumption, high frequency, and a compact size.

Pre-phase transition of a Cu2-xS template enables polymorph selective synthesis of MS (M = Zn, Cd, Mn) nanocrystals via cation exchange reactions.

Utilization of copper-deficient Cu2-xS nanocrystals (NCs) with diverse crystal phases and stoichiometries as cation exchange (CE) templates is a potential route to overcome the current limitations in the polymorph selective synthesis of desired nanomaterials. Among the Cu2-xS NCs, covellite CuS is emerging as an attractive CE template to produce complicated and metastable metal sulfide NCs. The presence of a reducing agent is essential to induce a phase transition of CuS into other Cu2-xS phases prior to the CE reactions. Nevertheless, the effect of the reducing agent on the phase transition of CuS, especially into the hexagonal close packing (hcp) phase and the cubic close packing (ccp) phase, has been scarcely exploited, but it is highly important for the polymorphic production of metal sulfides with the wurtzite phase and zinc blende phase. Herein, we report a reducing agent dependent pre-phase transition of CuS nanodisks (NDs) into hcp and ccp Cu2-xS NCs. 1-Dodecanethiol molecules and oleylamine molecules selectively reduced CuS NDs into hcp djurleite Cu1.94S NDs and ccp digenite Cu1.8S NCs. Afterward, the hcp Cu1.94S NDs and ccp Cu1.8S NCs were exchanged by Zn2+/Cd2+/Mn2+, and the wurtzite phase and the zinc blende phase of ZnS, CdS, and MnS NCs were produced. Without the pre-phase transition, direct CE reactions of CuS NDs are incapable of synthesizing the above wurtzite and zinc blende metal sulfide NCs. Therefore, our findings suggest the importance of the pre-phase transition of the CE template in polymorphic syntheses, holding great promise in the fabrication of other polymorphic nanomaterials with novel physical and chemical properties.

Factors influencing further vertebral height loss following percutaneous vertebroplasty in osteoporotic vertebral compression fractures: A 1-year follow-up study.

BACKGROUND: Osteoporotic vertebral compression fractures (OVCFs) contribute to back pain and functional limitations in older individuals, with percutaneous vertebroplasty (PVP) emerging as a minimally invasive treatment. However, further height loss post-PVP prompts investigation into contributing factors. AIM: To investigate the factors associated with further height loss following PVP with cement augmentation in OVCF patients. METHODS: A total of 200 OVCF patients who underwent successful PVP between January 2021 and December 2022 were included in this study. "Further height loss" during 1 year of follow-up in OVCF patients with bone edema was defined as a vertical height loss of ≥ 4 mm. The study population was divided into two groups for analysis: The "No Further Height Loss group (n = 179)" and the "Further Height Loss group (n = 21)." RESULTS: In comparing two distinct groups of patients, significant differences existed in bone mineral density (BMD), vertebral compression degree, prevalence of intravertebral cleft (IVF), type of bone cement used, and cement distribution patterns. Results from binary univariate regression analysis revealed that lower BMD, the presence of IVF, cleft distribution of bone cement, and higher vertebral compression degree were all significantly associated with further height loss. Notably, the use of mineralized collagen modified-poly(methyl methacrylate) bone cement was associated with a significant reduction in the risk of further height loss. In multivariate regression analysis, lower BMD and the presence of IVF remained significantly associated with further height loss. CONCLUSION: Further height loss following PVP in OVCF patients is influenced by a complex interplay of factors, especially lower BMD and the presence of IVF. These findings underscore the importance of assessing and managing these factors when addressing height loss following PVP in OVCF patients.

A discrete Huber-Braun neuron model: from nodal properties to network performance.

Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network. Supplementary Information: The online version contains supplementary material available at 10.1007/s11571-022-09806-1.

Chaos and multi-layer attractors in asymmetric neural networks coupled with discrete fractional memristor.

This article introduces a novel model of asymmetric neural networks combined with fractional difference memristors, which has both theoretical and practical implications in the rapidly evolving field of computational intelligence. The proposed model includes two types of fractional difference memristor elements: one with hyperbolic tangent memductance and the other with periodic memductance and memristor state described by sine functions. The authenticity of the constructed memristor is confirmed through fingerprint verification. The research extensively investigates the dynamics of a coupled neural network model, analyzing its stability at equilibrium states, studying bifurcation diagrams, and calculating the largest Lyapunov exponents. The results suggest that when incorporating sine memristors, the model demonstrates coexisting state variables depending on the initial conditions, revealing the emergence of multi-layer attractors. The article further demonstrates how the memristor state shifts through numerical simulations with varying memductance values. Notably, the study emphasizes the crucial role of memductance (synaptic weight) in determining the complex dynamical characteristics of neural network systems. To support the analytical results and demonstrate the chaotic response of state variables, the article includes appropriate numerical simulations. These simulations effectively validate the presented findings and provide concrete evidence of the system's chaotic behavior.

Obstacle induced spiral waves in a multilayered Huber-Braun (HB) neuron model.

Various dynamical properties of four-dimensional mammalian cold receptor model have been discussed widely in the literature considering noise and temperature as important parameters of discussion. Though various spiking and bursting behaviors of the neuron under various noise and temperature conditions studied for a single neuron, no much discussions have been done on the collective behavior. We investigate the collective behavior of these temperature dependent stochastic neurons and unlike the neuron models when forced by periodic external force there is no wave reentry or spiral waves in the network. Hence, we introduce obstacle in the network and depending on the orientation and size of the introduced obstacle, we could show their effects on the wave reentry in the network. Various significant discussions are produced in this paper to confirm that obstacles placed parallel to the wave entry affects the excitability of the tissues significantly compared to those obstacles place perpendicular. We could also show that those obstacles which are lesser in dimensions doesn't affect the excitabilities and hence doesn't contribute for wave reentry. We introduce a new technique to identify wave reentry and spiral waves using the period of individual nodes is proposed. This technique could help us identify even the lowest of excitability change which cannot be seen when using spatiotemporal snapshots.

[Application of augmented reality technique in repairing soft tissue defects of lower limbs with posterior tibial artery perforator flap].

Objective: To investigate the accuracy and reliability of augmented reality (AR) technique in locating the perforating vessels of the posterior tibial artery during the repair of soft tissue defects of the lower limbs with the posterior tibial artery perforator flap. Methods: Between June 2019 and June 2022, the posterior tibial artery perforator flap was used to repair the skin and soft tissue defects around the ankle in 10 cases. There were 7 males and 3 females with an average age of 53.7 years (mean, 33-69 years). The injury was caused by traffic accident in 5 cases, bruising by heavy weight in 4 cases, and machine injury in 1 case. The size of wound ranged from 5 cm×3 cm to 14 cm×7 cm. The interval between injury and operation was 7-24 days (mean, 12.8 days). The CT angiography of lower limbs before operation was performed and the data was used to reconstruct the three-dimensional images of perforating vessels and bones with Mimics software. The above images were projected and superimposed on the surface of the affected limb using AR technology, and the skin flap was designed and resected with precise positioning. The size of the flap ranged from 6 cm×4 cm to 15 cm×8 cm. The donor site was sutured directly or repaired with skin graft. Results: The 1-4 perforator branches of posterior tibial artery (mean, 3.4 perforator branches) in 10 patients were located by AR technique before operation. The location of perforator vessels during operation was basically consistent with that of AR before operation. The distance between the two locations ranged from 0 to 16 mm, with an average of 12.2 mm. The flap was successfully harvested and repaired according to the preoperative design. Nine flaps survived without vascular crisis. The local infection of skin graft occurred in 2 cases and the necrosis of the distal edge of the flap in 1 case, which healed after dressing change. The other skin grafts survived, and the incisions healed by first intention. All patients were followed up 6-12 months, with an average of 10.3 months. The flap was soft without obvious scar hyperplasia and contracture. At last follow-up, according to the American Orthopedic Foot and Ankle Association (AOFAS) score, the ankle function was excellent in 8 cases, good in 1 case, and poor in 1 case. Conclusion: AR technique can be used to determine the location of perforator vessels in the preoperative planning of the posterior tibial artery perforator flap, which can reduce the risk of flap necrosis, and the operation is simple.

Method Validation and Measurement Uncertainty (MU) Evaluation on Enrofloxacin and Ciprofloxacin in the Aquatic Products.

This study aimed to investigate a detection method of enrofloxacin and ciprofloxacin to be avail for strictly supervising the quality and safety of aquatic products. The results displayed that the optimal extraction conditions for enrofloxacin and ciprofloxacin were the following five aspects: 15 g dosages of Na2SO4 to dehydrate, 8‰ of acetonitrile and 50% hydrochloric acid to deproteinization, 2 mL dosages of n-hexane to degrease, 10 min of ultrasonic time, and 20 min of extraction (stand) time. Meanwhile, it was also obtained for the optimal detection performance indexes of the recovery, precision, and accuracy from the tests of shrimp, grass carp, and tilapia. In particular, the expanded uncertainties were 2.8601 and 0.8613, and the factors of both the calibration curves (Urel(C)) and the analysis of the experiment (Urel(E)) were the two MU main contributors for enrofloxacin and ciprofloxacin together with the results above 40%. Consequently, the developed novel method was suited for the determination of the enrofloxacin and ciprofloxacin residues in aquatic products and would contribute to reinforce in supervision and inspection of the quality and safety of aquatic products.