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This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

When modeling longitudinal data, the true values of time-varying covariates may be unknown because of detection-limit censoring or measurement error. A common approach in the literature is to empirically model the covariate process based on observed data and then predict the censored values or mismeasured values based on this empirical model. Such an empirical model can be misleading, especially for censored values since the (unobserved) censored values may behave very differently than observed values due to the underlying data-generation mechanisms or disease status. In this paper, we propose a mechanistic nonlinear covariate model based on the underlying data-generation mechanisms to address censored values and mismeasured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mismeasured values are more reasonable. We use a Monte Carlo EM algorithm for likelihood inference and apply the methods to an AIDS dataset, where viral load is censored by a lower detection limit. Simulation results confirm that the proposed models and methods offer substantial advantages over existing empirical covariate models for censored and mismeasured covariates. [ABSTRACT FROM AUTHOR]

In clinical trials and biomedical studies, treatments are compared to determine which one is effective against illness; however, individuals can react to the same treatment very differently. We propose a complete process for longitudinal data that identifies subgroups of the population that would benefit from a specific treatment. A random effects linear model is used to evaluate individual treatment effects longitudinally where the random effects identify a positive or negative reaction to the treatment over time. With the individual treatment effects and characteristics of the patients, various classification algorithms are applied to build prediction models for subgrouping. While many subgrouping approaches have been developed recently, most of them do not check its validity. In this paper, we further propose a simple validation approach which not only determines if the subgroups used are appropriate and beneficial but also compares methods to predict individual treatment effects. This entire procedure is readily implemented by existing packages in statistical software. The effectiveness of the proposed method is confirmed with simulation studies and analysis of data from the Women Entering Care study on depression. [ABSTRACT FROM AUTHOR]

We propose a method to improve biometric authentication systems using a multifactor approach. For this security scheme a user authenticates successfully using a set of three characteristics related to physical, possession and knowledge factors. Besides biometric authentication representing the physical factor, we propose the use of an optical authentication technique based on two-beam interference and chaotic maps. In this sense, the seed of a chaotic map represents a user password corresponding to a knowledge factor and a resultant interferogram from optical authentication technique is used as a possession factor. The feasibility of our method is tested using numerical simulation. Moreover, key space and statistical analysis are performed to demonstrate the effectiveness of the solution. [ABSTRACT FROM AUTHOR]

In many data-driven modeling, prediction or identification applications to unknown systems, linguistic (fuzzy) results described by fuzzy sets are more preferable than the crisp results described by numbers owing to the uncertainties and/or noises existed in the observed data. On the other hand, fuzzy neural network (FNN) provides a powerful tool for providing accurate crisp results, but does not have the ability to achieve linguistic outputs due to its crisp weights. This study extends the crisp weights of FNN to fuzzy ones to obtain linguistic outputs. And, a data-driven design method is proposed to construct this kind of fuzzily weighted FNN (FW-FNN). The proposed data-driven method includes four steps. Firstly, a fully connected FNN is generated. Then, the SVD-QR method based pruning strategy is presented to realize the structure reduction of the initial FW-FNN. Thirdly, the centers of the Gaussian fuzzy weights in the structure reduced FW-FNN are learned by the least square method. Fourthly, the multi-objective algorithm is utilized to optimize the widths of the Gaussian fuzzy weights to achieve the maximum of the average membership grades of the output fuzzy sets and the minimum of the coverage intervals of the linguistic outputs. To evaluate the proposedFW-FNN and the data-driven method, applications to the nonlinear dynamic system identification, the chaotic time series prediction and the traffic flowprediction are given. Simulation results demonstrate that the linguistic outputs can effectively capture the uncertainties and/or noises in the observed data. It provides us a very useful tool for system modeling, prediction and identification especially when uncertainties and/or noises should be taken into account. [ABSTRACT FROM AUTHOR]

A new asymmetric multiple information cryptosystem based on chaotic spiral phase mask (CSPM) and random spectrum decomposition is put forwarded. In the proposed system, each channel of secret color image is first modulated with a CSPM and then gyrator transformed. The gyrator spectrum is randomly divided into two complex-valued masks. The same procedure is applied to multiple secret images to get their corresponding first and second complex-valued masks. Finally, first and second masks of each channel are independently added to produce first and second complex ciphertexts, respectively. The main feature of the proposed method is the different secret images encrypted by different CSPMs using different parameters as the sensitive decryption/private keys which are completely unknown to unauthorized users. Consequently, the proposed system would be resistant to potential attacks. Moreover, the CSPMs are easier to position in the decoding process owing to their own centering mark on axis focal ring. The retrieved secret images are free from cross-talk noise effects. The decryption process can be implemented by optical experiment. Numerical simulation results demonstrate the viability and security of the proposed method. [ABSTRACT FROM AUTHOR]

Long length of stay and overcrowding in emergency departments (EDs) are two common problems in the healthcare industry. To decrease the average length of stay (ALOS) and tackle overcrowding, numerous resources, including the number of doctors, nurses and receptionists need to be adjusted, while a number of constraints are to be considered at the same time. In this study, an efficient method based on agent-based simulation, machine learning and the genetic algorithm (GA) is presented to determine optimum resource allocation in emergency departments. GA can effectively explore the entire domain of all 19 variables and identify the optimum resource allocation through evolution and mimicking the survival of the fittest concept. A chaotic mutation operator is used in this study to boost GA performance. A model of the system needs to be run several thousand times through the GA evolution process to evaluate each solution, hence the process is computationally expensive. To overcome this drawback, a robust metamodel is initially constructed based on an agent-based system simulation. The simulation exhibits ED performance with various resource allocations and trains the metamodel. The metamodel is created with an ensemble of the adaptive neuro-fuzzy inference system (ANFIS), feedforward neural network (FFNN) and recurrent neural network (RNN) using the adaptive boosting (AdaBoost) ensemble algorithm. The proposed GA-based optimization approach is tested in a public ED, and it is shown to decrease the ALOS in this ED case study by 14%. Additionally, the proposed metamodel shows a 26.6% improvement compared to the average results of ANFIS, FFNN and RNN in terms of mean absolute percentage error (MAPE). [ABSTRACT FROM AUTHOR]

This paper deals with the connection between longitudinal and transversal sections of the state space of chaotic events in the nonlinear damped and forced oscillator (NLDFO), which may be considered the drosophila of physical chaos. In order to extract the above mentioned sections, which are nothing but tomographies of state space, the Poincaré techniques of slicing the cited space have been applied. The longitudinal sections of state space display the period bifurcation cascade of the chaotic event and, its transversal sections show the attractors of the dynamics; these display evidence that even during the most furious stages of chaos, there is order and structure in the chaotic behavior of the oscillator. It has been found that the attractor of a complete chaotic event is made up of a series of partial strange attractors, one after another and, that the transition from one to the next is smooth, i.e., the end of an attractor gradually becomes the beginning of the next. This report includes also some conclusions of investigations carried out by this author in the NLDFO; since this system transitions to chaos through a cascade of period bifurcations, these conclusions may be generalized to those systems transitioning to chaos following the same route. [ABSTRACT FROM AUTHOR]

Synchronization between two Lorenz systems is analyzed through various forms of coupling between them. We have used direct, conjugate, delayed direct and delayed conjugate coupling mechanism. In each case Lyapunov exponent is computed for ascertaining the synchronized situation, which is then used to encrypt a signal and then retrieve the same by the second system. The situation is demonstrated with the help of electronic circuit. It is observed that both the numerical simulation and experimental results corroborates each other. Lastly the chaotic data from the circuit is also used to encrypt an image and retrieve by the second set. In both the cases the system security is discussed. [ABSTRACT FROM AUTHOR]

We demonstrate that chaos can be controlled and converted into periodic behaviour in photorefractive ring oscillator via nonlinear feedback and find that the period number differs on the account of the feedback strength. By increasing the feedback strength the photorefractive ring oscillator is converted into period 8 and subsequently into period 4, 2, and 1. Nonlinear feedback is suitable for both the photorefractive ring oscillator system and spatiotemporal system. Spatiotemporal chaos can be controlled into stable periodic states and stable spatial patterns if we choose suitable feedback strength. Furthermore we present the synchronization of spatiotemporal chaos in two photorefractive ring oscillator systems via nonlinear feedback technology. The synchronization of spatiotemporal chaos can be achieved by adjusting the feedback strength without any pre-knowledge of the dynamic system. Numerical calculation results show that weak noise has a slight impact on synchronization, so nonlinear feedback technology is suitable in practical photorefractive ring oscillator systems. [ABSTRACT FROM AUTHOR]

In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness. Finally, the comparative findings are discussed. [ABSTRACT FROM AUTHOR]

This article proposes and implements a class of chaotic motors for electric compaction. The key is to develop a design approach for the permanent magnets (PMs) of doubly salient PM (DSPM) motors in such a way that chaotic motion can be naturally produced. The bifurcation diagram is employed to derive the threshold of chaoization in terms of PM flux, while the corresponding phase-plane trajectories are used to characterize the chaotic motion. A practical three-phase 12/8-pole DSPM motor is used for exemplification. The proposed chaotic motor is critically assessed for application to a vibratory soil compactor, which is proven to offer better compaction performance than its counterparts. Both computer simulation and experimental results are given to illustrate the proposed chaotic motor. [ABSTRACT FROM AUTHOR]

Conditional power based on summary statistic by comparing outcomes (such as the sample mean) directly between 2 groups is a convenient tool for decision making in randomized controlled trial studies. In this paper, we extend the traditional summary statistic-based conditional power with a general model-based assessment strategy, where the test statistic is based on a regression model. Asymptotic relationships between parameter estimates based on the observed interim data and final unobserved data are established, from which we develop an analytic model-based conditional power assessment for both Gaussian and non-Gaussian data. The model-based strategy is not only flexible in handling baseline covariates and more powerful in detecting the treatment effects compared with the conventional method but also more robust in controlling the overall type I error under certain missing data mechanisms. The performance of the proposed method is evaluated by extensive simulation studies and illustrated with an application to a clinical study. [ABSTRACT FROM AUTHOR]

In this paper, a physical SBT memristor-based chaotic circuit is presented. The circuit dynamic behavior of dependence on the initial state of the SBT memristor and a key circuit parameter are investigated by theoretical analyses and numerical simulations. The results indicate that different initial states of the SBT memristor and the key circuit parameter can significantly impact the dynamic behavior of the chaotic circuit, such as stable sink, periodic cycle, chaos, and even some complex transient dynamics. It can guide future research on the realization of chaotic circuit based on physical SBT memristor. [ABSTRACT FROM AUTHOR]

Chaotic systems have been widely used in digital image encryption algorithms because of their characteristics of deterministic randomness, extreme sensitivity to initial values, etc. Although these chaos-based algorithms are good at performance in general, most of them are ineffective when confronting attacks such as the chosen plain image attack. So, this paper proposes a new digital image encryption algorithm based on orbit variation of phase diagram (AOVPD), which modifies the iterative sequence of chaotic system with the pixel values of plain image. Theoretical analysis proves that the proposed AOVPD has the ability to resist chosen plain image attack within two rounds of operation, while the existing algorithms could be cracked in the same situation. To be specific, AOVPD is effective when confronting various attacks including chosen plain image attack. Also, simulation results show that the proposed algorithm has an outstanding safety performance. [ABSTRACT FROM AUTHOR]

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of . Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, a new three-dimensional autonomous fractional-order chaotic system is presented. There are four different nonlinear terms in the governed equations. By means of theoretical analysis and numerical simulation, some basic dynamical properties, such as phase diagrams, bifurcation diagram, Lyapunov exponents spectrum and chaos diagram of the new fractional-order chaotic system are investigated. Then, we completed the circuit design of the fractional-order chaotic system, and realized the analog hardware circuit. Both the hardware experiment results and circuit simulation results are agreed well with those of numerical simulation. Finally, based on the theory of sliding-mode control and the fractional stability theory, a suitable sliding mode controller is designed for the novel three-dimensional fractional-order chaotic system. Numerical simulations are provided to verify the effectiveness of the proposed synchronization scheme. [ABSTRACT FROM AUTHOR]

We propose a Bayesian variable selection method in semi-parametric models with applications to genetic and epigenetic data (e.g., single nucleotide polymorphisms and DNA methylation, respectively). The data are individually standardized to reduce heterogeneity and facilitate simultaneous selection of categorical (single nucleotide polymorphisms) and continuous (DNA methylation) variables. The Gaussian reproducing kernel is applied to the transformed data to evaluate joint effect of the variables, which may include complex interactions between, e.g., single nucleotide polymorphisms and DNA methylation. Indicator variables are introduced to the model for the purpose of variable selection. The method is demonstrated and evaluated using simulations under different scenarios. We apply the method to identify informative DNA methylation sites and single nucleotide polymorphisms in a set of genes based on their joint effect on allergic sensitization. The selected single nucleotide polymorphisms and methylation sites have the potential to serve as early markers for allergy prediction, and consequently benefit medical and clinical research to prevent allergy before its manifestation. [ABSTRACT FROM AUTHOR]

In multiple fields of study, time series measured at high frequencies are used to estimate population curves that describe the temporal evolution of some characteristic of interest. These curves are typically nonlinear, and the deviations of each series from the corresponding curve are highly autocorrelated. In this scenario, we propose a procedure to compare the response curves for different groups at specific points in time. The method involves fitting the curves, performing potentially hundreds of serially correlated tests, and appropriately adjusting the overall alpha level of the tests. Our motivating application comes from psycholinguistics and the visual world paradigm. We describe how the proposed technique can be adapted to compare fixation curves within subjects as well as between groups. Our results lead to conclusions beyond the scope of previous analyses. [ABSTRACT FROM AUTHOR]

Modeling and simulation of chaotic system with dynamic control have been extensively presented in the past decades. Several control techniques have been proposed for the control of chaos. One technique that has not been sufficiently explored for the control of nonlinear systems is the controller identification technique. This technique is based on the evaluation of controllers even if they are not online. This technique does not use a priori knowledge of the plant parameters. In this work, we propose a class of controllers candidates to follow desired trajectories. Simulation results are presented for the control of chaotic systems. [ABSTRACT FROM AUTHOR]

In this study, a high gain observer with delayed driving control signal is designed for synchronisation of fractionalorder chaotic systems. The method consists in using two cascade high gain observers in order to compensate for the delay transmission signal from the transmitter to the receiver. For large delay, a fractional-order chain observer composed by high gain cascade delayed observers is proposed. The last observer of this chain estimates the state at the current time while previous observers estimate delayed states. Convergence of the proposed observer is proven. Application to the synchronisation of fractional-order chaotic systems is given. Computer simulations show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper provides a general framework for modifying chaotic systems on the premise of preserving chaos. It formulates effective techniques to construct some derivative systems from an existing chaotic system by replacing a parameter or a term in the dynamical system with certain time-dependent or state-dependent functions. This study derives an alternative for chaotic system construction and also provides more flexibility for chaotic synthesis. Numerical simulations demonstrate the effectiveness and validity of the proposed techniques. As a consequence, some new chaotic systems are also obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of the master–slave synchronization of chaotic Lur’e systems with multiple time delays in their states and transmission line. Based on the Lyapunov–Krasovskii functional, some delay-dependent synchronization criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the global asymptotic stability of the error system such that the slave system is synchronized with the master. With the help of the LMI solvers, the time-delay feedback control law can easily be obtained. The effectiveness of the proposed method is illustrated using some numerical simulations performed on two chaotic systems. [ABSTRACT FROM AUTHOR]

In future, since the user experience plays a more and more important role in the development of today's communication systems, quality of experience (QoE) becomes a widely used metric, which reflects the subjective experience of end users for wireless service. In addition, the energy efficiency is an increasingly important problem with the explosive growth in the amount of wireless terminals and nodes. Hence, a QoE-aware energy efficiency maximization based joint user access selection and power allocation approach is proposed to solve the problem. We transform the joint allocation process to an optimization of energy efficiency by establishing an energy efficiency model, and then the optimization problem is solved by chaotic clone immune algorithm (CCIA). Numerical simulation results indicate that the proposed algorithm can efficiently and reliably improve the QoE and ensure high energy efficiency of networks. [ABSTRACT FROM AUTHOR]

The boundedness of chaotic systems plays an important role in investigating the stability of the equilibrium, estimating the Lyapunov dimension of attractors, the Hausdorff dimension of attractors, the existence of periodic solutions, chaos control, and chaos synchronization. However, as far as the authors know, there are only a few papers dealing with bounds of high-order chaotic systems due to their complex algebraic structure. To sort this out, in this paper, we study the bounds of a high-order Lorenz-Stenflo system arising in mathematical physics. Based on Lyapunov stability theory, we show that there exists a globally exponential attractive set for this system. The innovation of the paper is that we not only prove that this system is globally bounded for all the parameters, but also give a family of mathematical expressions of global exponential attractive sets of this system with respect to its parameters. We also study some other dynamical characteristics of this chaotic system such as invariant sets and chaotic behaviors. To justify the theoretical analysis, we carry out detailed numerical simulations. [ABSTRACT FROM AUTHOR]

As a result of the simulation of the functions of the probability distribution in systems with chaos in the chemical composition, which also includes difficult natural and technogenic mixes, e.g., oil hydrocarbonic systems, it is established that the normal distribution of the composition is observed with the probability of differences in the components in the range of 0.2-0.8. This means that the normal distribution of free energy, and the boiling temperatures are achievable in systems where the ratio of the number of components with different properties to the total number of components is 20-80%. The borders of the difference probability are established, which define the belonging of systems to different types of distribution. At a share of the differing on properties components of 1-8.5%, the distribution is close to Poisson's distribution. When the differences in the probability components in range of 0.085-0.2, a region of unstable distribution is observed. [ABSTRACT FROM AUTHOR]

Compressive sensing is a new sampling theory which makes use of the sparsity of signals to recover the high-dimension signal from very few measurements. Unfortunately,most of the existing measurement matrices have high correlation between elements,which can not guarantee exact recovery and has greatly restricted their application prospects. Based on this,this paper proposed a novel Chebyshev chaotic measurement sensing matrix based on sampling columnization( SC3M). The sampling columnization and normalization guaranteed the low correlation in column of SC3 M,which optimized the recovery effect. Moreover,it proved that the proposed SC3 M sensing matrix satisfies the RIP with overwhelming probability from the Johnson-Lindenstrauss lemma. Numerical simulations show that the SC3 M is sufficient to guarantee exact recovery,which shows better effect compared to other popular measurement matrixes such as the fully random matrix,Bernoulli matrix and Gaussian sensing matrix. [ABSTRACT FROM AUTHOR]

In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PIλ control law with the fractional-order adaptive sliding mode controller in order to eliminate the chattering action in the control signal. Based on Lyapunov theory, the stability analysis of the proposed control strategy is performed for an acceptable synchronization error level. Numerical simulations illustrate the efficiency of the proposed fractional fuzzy adaptive control scheme through the synchronization of two different fractional order chaotic Duffing systems. We show that the introduction of the additional fractional adaptive PIλ control action is able to eliminate the chattering phenomena in the control signal. [ABSTRACT FROM AUTHOR]

Recent evidence suggests that there exists chaos in a few no-equilibrium systems. A chaotic system without equilibrium is proposed and studied in this work. It is worth noting that due to the absence of equilibrium, such a system belongs to a class of systems with hidden attractor. Dynamics properties and the feasibility of the system are investigated by using numerical simulations and circuit implementation. Interestingly, this no-equilibrium system has one variable with the freedom of offset boosting. [ABSTRACT FROM AUTHOR]

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system. [ABSTRACT FROM AUTHOR]

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed--the method based on conditional mutual information--the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping--the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved. [ABSTRACT FROM AUTHOR]

We study the influence of periodic influx on a character of glycolytic oscillations within the forced Selkov system. We demonstrate that such a simple system demonstrates a rich variety of dynamical regimes (domains of entrainment of different order (Arnold tongues), quasiperiodic oscillations, and chaos), which can be qualitatively collated with the known experimental data. We determine detailed dynamical regimes exploring the map of Lyapunov characteristic exponents obtained in numerical simulations of the Selkov system with periodic influx. In addition, a special study of the chaotic regime and the scenario of its origin in this system was evaluated and discussed. [ABSTRACT FROM AUTHOR]

It is often difficult to obtain the bounds of the hyperchaotic systems due to very complex algebraic structure of the hyperchaotic systems. After an exhaustive research on a new 4D Lorenz-type hyperchaotic system and a coupled dynamo chaotic system, we obtain the bounds of the new 4D Lorenz-type hyperchaotic system and the globally attractive set of the coupled dynamo chaotic system. To validate the ultimate bound estimation, numerical simulations are also investigated. The innovation of this article lies in that the method of constructing Lyapunov-like functions applied to the Lorenz system is not applicable to this 4D Lorenz-type hyperchaotic system; moreover, one Lyapunov-like function cannot estimate the bounds of this 4D Lorenz-type hyperchaos system. To sort this out, we construct three Lyapunov-like functions step by step to estimate the bounds of this new 4D Lorenz-type hyperchaotic system successfully. [ABSTRACT FROM AUTHOR]

This paper investigates the control problems of the Bose–Einstein condensate (BEC) system. Firstly, a new linear feedback control method for the control problems of a class of chaotic systems in any dimension based on triangle system structure. Then, based on the obtained method, the stabilization, synchronization, and anti-synchronization of BEC system are investigated extensively, and the corresponding controllers are designed. It should be pointed out that the obtained controllers are single input linear controllers, which are simpler than the existing results. Finally, numerical simulations are given to show the effectiveness and validity of the proposed results. [ABSTRACT FROM AUTHOR]

A simple method for suppressing chaos in a discrete dynamical system has been proposed by Guemez and Mathias and consists in applying regular proportional feedbacks in the system variables only. The success of the scheme seems to depend critically on the strength and the period of the feedback. Unfortunately, the paucity of the reported results prevents the interested reader to appreciate the effectiveness of the technique. The present paper intends to fill this gap by providing an important number of numerical proofs that demonstrate without any doubt the method is able to stabilize an impressive number of ordered orbits, of different periods, often only with a small intervention in the system variables. Some additional aspects, including the mechanisms of transition from chaos to order and vice-versa, the distance between two successive interventions or the influence of the system degree of chaoticity on the percentages of success in stabilizing a periodic orbit, are also investigated. The numerical simulations have been performed on the logistic map but similar results can be obtained on other unidimensional maps. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a generalized anti-synchronization of coupled different hyperchaotic systems via linear transformation. The necessary and sufficient condition for generalized anti-synchronization of coupled hyperchaotic systems are derived. We consider two different hyperchaotic Lorenz-Stenflo and Rössler system for generalized anti-synchronization scheme for bidirectionally coupled chaotic systems. Numerical simulations are presented to show the effectiveness of our proposed scheme. [ABSTRACT FROM AUTHOR]

The three-dimensional flow past an inclined circular disk is investigated using direct numerical simulations. Various incidence angles of the disk with respect to the inflow are considered from 0 ° to 60 ° , where 0 ° refers to the condition in which the flow is perpendicular to the disk. The aspect ratio (diameter/thickness) of the disk is considered to be 50. The Reynolds number based on the inflow velocity and the diameter of the disk is up to 500. The drag and lift coefficients, pressure coefficients, and three-dimensional vortical structures are analyzed using time-dependent and time-averaged techniques. Detailed comparisons between the results of the disk at different incidence angles are presented. The flow pattern gradually changes from chaotic to a periodic state as the incidence angle increases from 0 ° to 60 ° . At incidence angles of 45 ° and 50 ° , an evident low-frequency modulation exists whose period is approximately ten times greater than the primary vortex shedding period. For the inclined disks, the wake flow is tilted to the trailing edge side of the disk rather than parallel to the streamwise direction. The distance between two successive vortical rings is observed to decrease as the incidence angle increases. The streamwise length of the mean recirculation bubble decreases as the incidence angle increases. [ABSTRACT FROM AUTHOR]

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos. [ABSTRACT FROM AUTHOR]

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making efficient quantification and propagation of uncertainties an important aspect. In this context, a typical workflow includes the characterization of the uncertainty in the input variables. In this paper, input variables are modelled by probability-boxes (p-boxes), accounting for both aleatory and epistemic uncertainty. The propagation of p-boxes leads to p-boxes of the output of the computational model. A two-level meta-modelling approach is proposed using non-intrusive sparse polynomial chaos expansions to surrogate the exact computational model and, hence, to facilitate the uncertainty quantification analysis. The capabilities of the proposed approach are illustrated through applications using a benchmark analytical function and two realistic engineering problem settings. They show that the proposed two-level approach allows for an accurate estimation of the statistics of the response quantity of interest using a small number of evaluations of the exact computational model. This is crucial in cases where the computational costs are dominated by the runs of high-fidelity computational models. [ABSTRACT FROM AUTHOR]

This paper investigates the observer design problem for 1D wave equation with nonlinear boundary condition containing a forcing term, whose dynamics presents spatiotemporal chaotic behaviors. By introducing a linear error input on the left-end boundary, we construct an observer via themethod of characteristics. Moreover, we present a sufficient and necessary condition for the stability of the error dynamics system. Numerical simulations are presented to illustrate the theoretical outcomes. [ABSTRACT FROM AUTHOR]

A Hopfield associative memory (HAM) is a major model of associative memory using neural networks. The classical HAM model has a low storage capacity. A pseudo-orthogonalized HAM (POHAM) was therefore proposed to improve storage capacity by encoding the training patterns to be pseudo-orthogonal. In the present work, we examine a different property of POHAM. A chaotic HAM (CHAM) can explore embedded patterns, including training patterns. Although it is not desirable to recall patterns other than training patterns, at a minimum, the reversed patterns are recalled. A POHAM regards the training and reversed patterns as equivalent. To take advantage of this property, we propose a chaotic POHAM (CPOHAM). We evaluated a CHAM and a CPOHAM using computer simulations. The CPOHAM never recalled the reversed patterns. In addition, the CPOHAM recalled very few other pseudo-memories, such as mixture patterns, due to the orthogonality of the encoded training patterns, while the CHAM frequently recalled the mixture patterns. [ABSTRACT FROM AUTHOR]

We report the appearance of three-dimensional (3D) multiheaded chimera states that display cascades of self-organized spatiotemporal patterns of coexisting coherence and incoherence. We demonstrate that the number of incoherent chimera domains can grow additively under appropriate variations of the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for the Kuramoto model of N identical phase oscillators placed in the unit 3D cube with periodic boundary conditions, parameters being the coupling radius r and phase lag α. To obtain the multiheaded chimeras, we perform the so-called 'cloning procedure' as follows: choose a sample single-headed 3D chimera state, make appropriate scale transformation, and put some number of copies of them into the unit cube. After that, start numerical simulations with slightly perturbed initial conditions and continue them for a sufficiently long time to confirm or reject the state existence and stability. In this way it is found, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoil knots admit this sort of multiheaded regeneration. On the other hand, multiple 3D chimeras without spiral rotations, like coherent and incoherent balls, tubes, crosses, and layers appear to be unstable and are destroyed rather fast even for arbitrarily small initial perturbations. [ABSTRACT FROM AUTHOR]