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A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

Peridynamics theory is a nonlocal meshless method that replaces differential equations with spatial integral equations, and has shown good applicability and reliability in the analysis of discontinuities. Further, with characteristics of clear physical meaning and simple and reliable numerical calculation, the bond-based peridynamics method has been widely applied in the field. However, this method describes the interaction between material points simply using a single elastic “spring”, and thus leads to a fixed Poisson’s ratio, relatively low computational efficiency and other inherent problems. As such, the goal of this review paper is to provide a summary of the various methods of bond-based peridynamics modeling, particularly those that have overcome the limitations of the Poisson’s ratio, considered the shear deformation and modeling of two-dimensional thin plates for bending and three-dimensional anisotropic composites, as well as explored coupling with finite element methods. This review will determine the advantages and disadvantages of such methods and serve as a starting point for researchers in the development of peridynamics theory.

We briefly present lag sequential analysis for behavioral streams, a commonly used method in psychology for quantifying the relationships between two nominal time series. Cross recurrence quantification analysis (CRQA) is shown as an extension of this technique, and we exemplify this nominal application of CRQA to eye-movement data in human interaction. In addition, we demonstrate nominal CRQA in a simple coupled logistic map simulation used in previous communication research, permitting the investigation of properties of nonlinear systems such as bifurcation and onset to chaos, even in the streams obtained by coarse-graining a coupled nonlinear model. We end with a summary of the importance of CRQA for exploring the relationship between two behavioral streams, and review a recent theoretical trend in the cognitive sciences that would be usefully informed by this and similar nonlinear methods. We hope this work will encourage scientists interested in general properties of complex, nonlinear dynamical systems to apply emerging methods to coarse-grained, nominal units of measure, as there is an immediate need for their application in the psychological domain.

In this paper scalar macroscopic models for traffic and pedestrian flows are coupled and the resulting system is investigated numerically. For the traffic flow the classical Lighthill–Whitham Richards model on a network of roads and for the pedestrian flow the Hughes model are used. These models are coupled via terms in the fundamental diagrams modeling an influence of the traffic and pedestrian flow on the maximal velocities of the corresponding models. Several physical situations, where pedestrians and cars interact, are investigated.

Bonhöffer–van der Pol(BVP) oscillator is a classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region, create the double scroll attractor due to the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in the experimental laboratory.

In the search for photosensitizers based on 5,10,15,20-tetrakis(3-hydroxyphenyl)porphyrin (m-THPP, 1), a novel series of asymmetric A₃B porphyrin molecules with oxyacetamide linkers have been synthesized. A facile synthetic route was followed through the reaction of m-THPP derived porphyrin monoacid with amino-heterocyclic molecules in the presence of HBTU/DIPEA coupling reagent to obtain the respective porphyrin conjugates 7-10, 16, 18 in satisfactory yields 30–76%. The structures of all compounds were confirmed by the means of ¹H, ${}^{13}$C NMR and by mass spectrometry (MALDI-TOF). The absorption and emission spectra of the synthesized porphyrin conjugates were displayed in methanol and showed high extension coefficient values. These preliminary studies could qualify these new candidates in being added to the porphyrin library for photomedicine applications.

We consider the coupling of two-dimensional (2D) and one-dimensional (1D) models to form a single hybrid 2D–1D model for time-dependent linear wave problems. The 1D model is used to represent a 2D computational domain where the solution behaves approximately in a 1D way. This hybrid model, if designed properly, is a more efficient way to solve the full 2D model over the entire problem. Two important issues related to such hybrid 2D–1D models are (a) the design of the hybrid model and its validation (with respect to the original problem) and (b) the way the 2D–1D coupling is done, and the coupling error generated. This paper focuses on the second issue. The method used in this paper to couple the 1D and 2D models is the one proposed by Panasenko. This method has been used for mixed-dimensional coupling in many steady-state problems, and here it is being used for the first time for time-dependent problems. The hybrid formulation is derived, and the numerical accuracy and efficiency of the method are explored for a couple of basic problems.

We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic dynamics such as frequency synchronization and phase synchronization, where the degree of synchronization can be quantified by the ratio of the interspike interval of the two excitable neural populations and the phase synchronization index, respectively. The stochastic synchronization can be either enhanced or suppressed by local time-delayed feedback control, depending upon the delay time and the coupling strength. The control depends crucially upon the coupling scheme of the control force, i.e., whether the control force is generated from the activator or inhibitor signal, and applied to either component. For inhibitor self-coupling, synchronization is most strongly enhanced, whereas for activator self-coupling there exist distinct values of the delay time where the synchronization is strongly suppressed even in the strong synchronization regime. For cross-coupling strongly modulated behavior is found.

In power line communication (PLC), coupling transformers are usually required for coupling, band-pass filtering and impedance matching. However, coupling transformer design involves so many parameters that it is typically an imprecise and experimental procedure. In addition, the cost and size of transformers prevent them from being an economic and compact solution for PLC couplers. This paper first analyzes a simplified, distributed parameter model of the power line, which can be used to calculate power line impedance easily and accurately. Next, a low-cost, band-pass matching coupler with compact architecture is designed to replace the coupling transformer for direct current PLC (DC-PLC), which ensures impedance matching on the basis of an accurate power line impedance instead of using an average value. Finally, simulations as well as laboratory tests are conducted under 95–125kHz (CENELEC B-band), which confirm the new coupler’s excellent band-pass filtering and impedance matching performance.

In this work, we extend the one-dimensional Keller–Segel model for chemotaxis to general network topologies. We define appropriate coupling conditions ensuring the conservation of mass and show the existence and uniqueness of the solution. For our computational studies, we use a positive preserving first-order scheme satisfying a network CFL condition. Finally, we numerically validate the Keller–Segel network model and present results regarding special network geometries.

By constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigroup associated with a class of degenerate functional stochastic differential equations.

We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential mixing. Leveraging from the structure of the associated correlation estimates, we prove an almost sure invariance principle for vector-valued observables. The motivation for our paper is to explore these methods in a non-uniform random setting.

Computational simulation of the thermal transport phenomena in the human body has recently aroused a great deal of interest among researchers, because it can be applied in different areas such as medicine, rehabilitation, space suits, and others. In this study, we developed a coupling model to analyze the temperature distribution of the human middle finger. Firstly, a one-dimensional thermo-fluid model of blood circulation in the human upper limb is constructed. Secondly, a two-dimensional thermal model of the human finger, which consists of skin, tendon, bone, main arteries, and veins is developed. The two models are further coupled weakly through data transfer. The blood pressure, blood flow rate, and blood temperature at different vessel sites and the tissue temperature are thus obtained. The effect of viscosity on the finger skin temperature was also investigated. Simultaneously, the thermograms of the human hand were also obtained using thermograpy under the resting condition and after jogging, to observe the variation in the blood circulation. The temperature at different points was extracted from the thermograms. It is observed that there is a periodic variation in skin temperature near the blood vessels after jogging. It is expected that this coupling model will be applicable to hyperthermia, drug delivery, and sports training.

The coupling effect of seepage and temperature fields in fractured rock mass is a hot topic in the area of water conservancy, nuclear waste disposal and geothermal resources development. A coupling mathematical model of the seepage, flow temperature and rock mass temperature fields in the fracture network of rock mass is established based on the seepage and temperature interaction. A calculation program is developed and applied to calculate the seepage and temperature fields of the dam foundation of a water conservancy project. The interaction mechanism of the seepage, flow temperature and rock mass temperature fields is analyzed in this paper. Results show that the seepage field largely influences the temperature field, which can provide several suggestions for the deep underground disposal of nuclear waste, geothermal resources development and fractured rock mass in dam foundations. Considering the coupling effect of the seepage, flow temperature and rock mass temperature fields by the fracture network method is necessary.

For the quantification of strength and identification of direction of coupling between two sub-systems of a complex dynamical system, observed from bivariate time series, a number of measures have been proposed that can be grouped in measures of phase synchronization, state space and information. We review all these measures and, in particular, for the information measures we examine different estimates of the probability distributions. We propose also a modification of the transfer entropy measure to span larger time windows and thus be more appropriate for flows. Simulations on systems of different types and for varying coupling strengths showed that information measures, and the modified transfer entropy measure in particular, detect best the coupling strength and direction. This is also found when applying the measures to pairs of EEG channels in order to detect the propagation of pre-epileptic brain activity.

The mechanism of formation and transformation of white-eye square patterns in dielectric barrier discharge system is investigated numerically, using the two-layer Lengyel–Epstein model with asymmetric and symmetric coupling. When the scale of the simulation system $N$ is two to three times of pattern wavelength $\lambda$, it is found that an obvious intermediate state with square distribution appears by adjusting the ratio of diffusion coefficients $D_v$/$D_u$. When it is coupled with a suitable short-wavelength Turing mode in the range of $\lambda /6$ to $\lambda /5$, a new spatial resonance structure can be formed in the short-wavelength mode subsystem, and the pattern evolves from a simple square pattern to a white-eye square pattern. Although the two coupling methods achieve the same results, the duration time of the white-eye square pattern in the symmetric coupling method is significantly longer than that in the asymmetric coupling method. Because the quadratic coefficient of the amplitude equation in the reaction–diffusion system is not zero, the simple square pattern of the long wavelength mode subsystem gradually transits into a stable hexagon pattern gradually. As a result, the white-eye pattern transits from a square to a hexagon.

In many signal processing applications, especially in the analysis of complex physiological systems, an important problem is to detect and quantify the interdependencies between signals (or time series). In this paper, we focus on asymmetrical relations between two time series with the aim of quantification of the directional influences between them in the sense of "who drives whom and how strongly". To meet this aim, we modify the mixed state analysis, which was proposed by Wiesenfeldt et al. [2001] to detect primarily the nature of the coupling (unidirectional or bidirectional), for the quantification of the strength of coupling in each direction. We introduce the predictability improvement of one time series by additional consideration of another time series. The newly developed measure is an analogue of the information theoretic concept of transfer entropy and is applicable to short time series. We demonstrate the application of this approach to coupled deterministic systems and to EEG data.

Traditional Boolean networks consist of nodes within a single network, each updating synchronously, although asynchronous versions have also been presented. In this paper the dynamics of two, mutually coupled traditional networks are investigated. In particular, the effects of varying the degree and type of intra-network connectivity are explored. The effects from different inter-network evolution rates are then considered, i.e. asynchronousity at the network level is examined. Finally, state memory is included within the nodes of coupled networks and shown to alter the dynamics of the networks under certain circumstances.

We discuss the synchronization of coupled neurons which are modeled as FitzHugh–Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting neural populations. Each system is prepared in the excitable regime and subject to independent random fluctuations. In order to modify their cooperative dynamics, we apply a local external stimulus in the form of an extended time-delayed feedback loop that involves multiple delays weighted by a memory parameter and investigate if the local control applied to a subsystem can allow one to steer the global cooperative dynamics. Depending on the choice of this new control parameter, we investigate different measures to quantify the influence on synchronization: ratio of interspike intervals, power spectrum, interspike interval distribution and phase synchronization intervals. We show that the control method is more robust for increasing memory parameter.

Code reuse has become very popular among software developers in recent times since it saves time and resources. One of the significant difficulties to software reuse is the time pertaining to assess the fitness of the reusable code components. Over the recent years, code search engines have made momentous advancement in establishing the semantic suitability of software components for new usage scenarios. But the issue of evaluating software components based on their nonfunctional suitability has been overlooked to a large extent. The maintenance and reusability of software systems are highly influenced by the structural properties of system classes like complexity, size, coupling, cohesion, etc. The quality of object-oriented code or design artifacts is commonly measured by analyzing the structure of these artifacts in terms of the interdependencies of classes and components as well as their internal elements. In this paper, we perform an empirical analysis on Python packages for the two measures namely coupling and cohesion. The coupling score of a module is computed as module imports and the cohesion score of a module is evaluated as call dependency between classes and global functions of the module. Finally, the proposed work evaluates a package in terms of reusability score which is a cumulative score of the coupling scores and cohesion scores of all the modules within the package. The study has evaluated 15 different packages and five different releases of one single package for reusability. We have empirically tested that the Halstead’s effort metric is inversely proportional to the reusability score. The reusability score was validated using four code detuners. The proposed work was compared with the existing metrics namely cyclomatic complexity and maintainability Index showing satisfactory results.