Search results

The purpose of this paper is to construct a proportion-integral-type (PI-type) memristor, which is different from that of the previous memristor emulator, but the constructing memristive chaotic circuit possesses line equilibrium, leading to the emergence of the initial conditions-related dynamical behaviors.

This paper presents a PI-type memristor emulator-based canonical Chua’s chaotic circuit. With the established mathematical model, the stability region for the line equilibrium is derived, which mainly consists of stable and unstable regions, leading to the emergence of bi-stability because of the appearance of a memristor. Initial conditions-related dynamical behaviors are investigated by some numerically simulated methods, such as phase plane orbit, bifurcation diagram, Lyapunov exponent spectrum, basin of the attraction and 0-1 test. Additionally, PSIM circuit simulations are executed and the seized results validate complex dynamical behaviors in the proposed memristive circuit.

The system exhibits the bi-stability phenomenon and demonstrates complex initial conditions-related bifurcation behaviors with the variation of system parameters, which leads to the occurrence of the hyperchaos, chaos, quasi-periodic and period behaviors in the proposed circuit.

These memristor emulators are simple and easy to physically fabricate, which have been increasingly used for experimentally demonstrating some interesting and striking dynamical behaviors in the memristor-based circuits and systems.

The paper shows that it is possible to reconstruct the dynamical attractors of demand at different levels of the supply chain by using time series duplication and techniques for normalisation. The objective of reconstructing dynamical attractors is to learn more about the long‐term dynamical behaviour of supply chains. Typical patterns that can be encountered through phase space reconstruction are discussed. Based on the analysis of real life supply chains first results are presented on how attractors can be used to better understand the dynamical behaviour of supply chains. The cases show that clear attractors can be identified for consumer and retailer demand. When this demand is compared with supply the phase space analysis becomes an effective tool for identifying distortion in the supply chain. The paper concludes by presenting two examples on how a better understanding of demand attractors have been used to improve operational and tactical planning.

Consumers are inclined to join longer queues due to social interactions in service consumptions. This purchase behavior brings in operational challenges in terms of capacity planning, which affects consumers’ demand, leading to an unstable and fluctuated arrival process. This paper aims to investigate the dynamic characteristics of the arrival process of a service system with boundedly rational consumers whose purchase decisions are influenced by the queue length under social interactions.

Consumers’ bounded rationality is modeled based on the random utility theory. Due to social interactions, the equilibrium queue length and its interaction with the expected waiting time affect consumers’ value perception. The authors first analyze the optimal service capacity decision with or without considering the influence of social interactions in a static setting. They then focus on the dynamic characteristics of the arrival process by a one-dimensional dynamical model in terms of the arrival rate.

This paper finds that the service system can behave chaotic in terms of arrival rate dynamics under social interactions. The results highlight the dynamical complexity of a simple service system due to consumers’ behavioral factors and the influence of social interactions, which may be the critical drivers leading to fluctuated and uneven demand.

The findings demonstrate that due to consumers’ limited cognitive ability and the influence of social interactions, the demand to a service system can be stable, periodic or even chaotic in terms of the arrival process. This study provides an alternative explanation to the observed demand fluctuations in various service processes under the influence of social interactions, which is important for service providers to effectively manage service capacity to achieve a stable service process and improve operational efficiency.

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few variables. Further, the simpler model very often displays oscillatory behavior of some sort, especially when critical problem parameters are varied in certain ranges. This paper attempts to supply arguments from the theory of dynamical systems for why oscillatory behavior is so frequently observed and to show how such behavior emerges as a natural consequence of focusing attention upon so‐called “essential” variables in the process of model simplification. The relationship of model simplification and oscillatory behavior is shown to be inextricably intertwined with the problems of bifurcation and catastrophe in that the oscillations emerge when critical system parameters, i.e. those retained in the simple model, pass through critical regions. The importance of the simplification, oscillation and bifurcation pattern is demonstrated here by consideration of several examples from the environmental, economic and urban areas.

This paper aims to study the complex behavior of a dynamical system using fractional and fractal-fractional (FF) derivative operators. The non-classical derivatives are extremely useful for investigating the hidden behavior of the systems. The Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) derivatives are considered for the fractional structure of the model. Further, to add more complexity, the authors have taken the system with a CF fractal-fractional derivative having an exponential kernel. The active control technique is also considered for chaos control.

The systems under consideration are solved numerically. The authors show the Adams-type predictor-corrector scheme for the AB model and the Adams–Bashforth scheme for the CF model. The convergence and stability results are given for the numerical scheme. A numerical scheme for the FF model is also presented. Further, an active control scheme is used for chaos control and synchronization of the systems.

Simulations of the obtained solutions are displayed via graphics. The proposed system exhibits a very complex phenomenon known as chaos. The importance of the fractional and fractal order can be seen in the presented graphics. Furthermore, chaos control and synchronization between two identical fractional-order systems are achieved.

This paper mentioned the complex behavior of a dynamical system with fractional and fractal-fractional operators. Chaos control and synchronization using active control are also described.

As compared with homogeneous metals and alloys, cellular metals provide low density, high specific stiffness, high energy absorption and good damping, thus being interesting alternatives to employ as protection against shock and impact. Impact energy is dissipated through cell bending, buckling or fracture. The knowledge and computational modelling of the mechanical behaviour of metal foams structures is thus of great importance for real life applications. The purpose of this paper is to increase the knowledge of the differences in metallic hollow sphere structures' (MHSS) behaviour under dynamic loading, as compared with the corresponding behaviour under static loading and to determine the influence of inertia and loading rate.

Computational dynamical finite element analyses of representative volume elements (RVE) of MHSS have been performed considering varying loading rates. Partially bonded geometries are considered and the effect of the spheres' distribution is also taken into account.

The results of the numerical examples presented show that inertia plays an important role in the dynamic behaviour of this kind of energy‐absorbing structure. When compared with the corresponding values in the quasi‐static case, the effect of inertia makes the peak load higher. If the deformation rate is higher (greater than 1.39 m/s in the studied cases), the characteristic plateau usually present in compressed metal foams can vanish. For the geometries analysed, damage has a small influence on load‐deformation relations.

This paper presents and discusses differences between static and dynamic behaviour of partially bonded MHSS. There are few references in the literature covering this issue by means of numerical analysis.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

Aims to analyse unique deformation properties of textile materials in terms of basic mechanical properties. Models fabric deformation as a nonlinear dynamical system so that a fabric can be completely specified in terms of its mechanical behaviour under general boundary conditions. Fabric deformation is dynamically analogous to waves travelling in a fluid. A localized two‐dimensional deformation evolves through the fabric to form a three‐dimensional drape or fold configuration. The nonlinear differential equations arising in the analysis of fabric deformation belong to the Klein‐Gordon family of equations which becomes the sine‐Gordon equation in three dimensions. The sine‐Gordon equation has its origins in the study of Bäcklund Transformations in differential geometry. Describes fabric deformation as a series of transformations of surfaces, defined in terms of curvature parameters using Gaussian representation of surfaces. By considering a deformed fabric as a two‐dimensional surface, algebraically constructs analytical solutions of fabric deformation by solving the sine‐Gordon Equation. The theory of Bäcklund Transformations is used to transform a trivial solution into a series of solitary wave solutions. These analytical expressions describing the curvature parameters of a surface represent actual solutions of fabric dynamical systems.

The purpose of this paper is to identify potential competitive relationships among brands by analyzing the dynamic clicking behavior of consumers.

Consumer sequential online click data, collected from JD.com, is used to analyze the dynamic competitive relationship between brands. It is found that the competition intensity across categories of products can differ considerably. Consumers exhibit big differences in purchasing time of durable-like goods, that is, the purchasing probability of such products changes considerably over time. The local polynomial regression model (LPRM) is used to analyze the relationship between brand competition of durable-like goods and the purchasing probability of a particular brand.

The statistical results of collective behaviors show that there is a 90/10 rule for the category durable-like goods, implying that ten percent of the brands account for 90 percent market share in terms of both clicking and purchasing behavior. The dynamic brand cognitive process of impulsive consumers displays an inverted V shape, while cautious consumers display a double V shaped cognitive process. The dynamic consumers’ cognition illustrates that when the brands capture a half of the click volume, the brands’ competitiveness reaches to its peak and makes no significant different from brands accounting for 100 percent of the click volume in terms of the purchasing probability.

There are some limitations to the research, including the limitations imposed by the data set. One of the most serious problems in the data set is that the collected click-stream is desensitized severely, restricting the richness of the conclusions of this study. Second, the data set consists of many other consumer behavioral data, but only the consumer’s clicking behavior is analyzed in this study. Therefore, in future research, the parameters brand browsing by consumers and the time of browsing in each brand should be added as indicators of brand competitive intensity.

The authors study brand competitiveness by analyzing the relationship between the click rate and the purchase likelihood of individual brands for durable-like products. When the brand competitiveness is less than 50 percent, consumers tend to seek a variety of new brands, and their purchase likelihood is positively correlated with the brand competitiveness. Once consumers learn about a particular brand excessively among all other brands at a period of time, the purchase likelihood of its products decreases due to the thinner consumer’s short-term loyalty the brand. Till the brand competitiveness runs up to 100 percent, consumers are most likely to purchase a brand and its product. That indicates brand competitiveness maintain 50 percent of the whole market is most efficient to be profitable, and the performance of costing more to improve the brand competitiveness might make no difference.

There are many studies on brand competition, but most of these research works analyze the brand’s marketing strategy from the perspective of the company. The limitation of this research is that the data are historical and failure to reflect time-variant competition. Some researchers have studied brand competition through consumer behavior, but the shortcoming of these studies is that it does not consider sequentiality of consumer behavior as this study does. Therefore, this study contributes to the literature by using consumers’ sequential clicking behavior and expands the perspective of brand competition research from the angle of consumers. Simultaneously, this paper uses the LPRM to analyze the relationship between consumer clicking behavior and brand competition for the first time, and expands the methodology accordingly.