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This paper considers supply chain management organizations with the aid of 'chaotic systems theory' developed originally in physics and mathematics. Since innovations in supply chain management are vital for organizational survival 'complex systems theory' may assist in fine-tuning managerial philosophies that provide stability in supply chain management because it is on the boundary of chaos that the greatest innovational creativity occurs. Neither 'management by rigid objectives' (MBO) nor 'management by instruction' (MBI) will be suitable for the information society of the twenty-first century because chaotic social systems will no longer be effectively managed. However, the capacity for self-organization will be derived essentially from how supply chain management members accept a shared set of values or principles for action-'management by values' (MBV). Complex systems theory deals with systems that show complex structures in time or space, often hiding simple deterministic rules. This theory holds that once these rules are found, it is possible to make effective predictions and even to control the apparent complexity. The state of chaos that self-organizes is attributable to the appearance of the 'strange attractor' and provides the ideal basis for creativity and innovation in the twenty-first century. In the self-organized state of chaos, social members are not confined to narrow roles and gradually develop their capacity for differentiation and relationships, growing progressively towards their maximum potential contribution to the efficiency of the organization. In this meaning, values act as organizers of 'attractors' of disorder, which, in the theory of chaos, are systems represented by usually regular geometric configurations that predict the long-term behavior of complex systems. In supply chain management organizations (as in all kinds of social systems) the initial principles end up as the final principles in the long term. An attractor is a model representation of the behavioral results of the system. The attractor is not a force of attraction or a goal-oriented presence in the system; it simply depicts where the system is heading based on its rules of motion. In supply chain management organizations that cultivate or shares values of autonomy, responsibility, independence, innovation, creativity, and proactivity, the risk of short-term chaos is mitigated by external complexities that organizations are currently confronting. The strategy is to alter the supply chain management's surroundings so that they can benefit from management by values (MBV).

The purpose of the study is to obtain explicit formulas to determine the stability of periodic solutions to the new system and study the extent of the stability of those periodic solutions and the direction of bifurcated periodic solutions. More than that, the authors did a numerical simulation to confirm the results that the authors obtained and presented through numerical analysis are the periodic and stable solutions and when the system returns again to the state of out of control.

The authors studied local bifurcation and verified its occurrence after choosing the delay as a parameter of control in Zhou 2019’s dynamical system with delayed feedback control. The authors investigated the normal form theory and the center manifold theorem.

The occurrence of local Hopf bifurcations at the Zhou's system is verified. By using the normal form theory and the center manifold theorem, the authors obtain the explicit formulas for determining the stability and direction of bifurcated periodic solutions. The theoretical results obtained and the corresponding numerical simulations showed that the chaos phenomenon in the Zhou's system can be controlled using a method of time-delay auto-synchronization.

As the delay increases further, the numerical simulations show that the periodic solution disappears, and the chaos attractor appears again. The obtained results can also be applied to the control and anti-control of chaos phenomena of system (1). There are still abundant and complex dynamical behaviors, and the topological structure of the new system should be completely and thoroughly investigated and exploited.

The purpose of this paper is to address the problem of control in a typical chaotic power system. Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not be controlled by adding the traditional controllers. So, the sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of the power system, eliminating control signal chattering and also show less control effort in comparison with the methods considered in previous literatures.

The sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory.

Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of power system, eliminating control signal chattering and also less control effort in comparison with the methods considered in previous literatures.

Main contributions of the paper are as follows: the chaotic behavior of power systems with two uncertainty parameters and tracking reference signal for the control of generator angle and the controller signal are discussed; designing sliding mode control based on a fuzzy supervisor in order to practically implement for the first time; while the generator speed is constant, the proposed controller will enable the power system to go in any desired trajectory for generator angle at first time; stability of the closed-loop sliding mode control based on the fuzzy supervisor system is proved using the Lyapunov stability theory; simulation of the proposed controller shows that the chattering is low control signal.

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.

The purpose of this paper is to investigate the impact of price adjustment speed on the stability of Bertrand–Nash equilibrium in the context of a dual-channel supply chain competition.

The paper considers a dual-channel supply chain comprising a manufacturer, a traditional retailer and an online retailer. A two-dimensional discrete dynamical system is used to examine the Bertrand competition between the retailers. The retailers are assumed to follow bounded rational expectations. Local stability of Bertrand–Nash equilibrium is investigated with respect to the price adjustment speed.

As the price adjustment speed increases, the stability of Bertrand–Nash equilibrium is lost, leading to complex chaotic dynamics. The results showed that chaotic dynamics deteriorates the profit of the retailers. The authors also found that the chaos can be controlled using an adaptive adjustment mechanism and the retailers enjoy higher profit when the chaos is controlled.

This study helps retail managers to choose an appropriate price adjustment speed to maximize profit.

The heterogeneity of the retailers is not considered in the studies involving dynamics of retailer competition. This paper contributes to the literature by considering the operational difference between a traditional retailer and an online retailer, i.e. price adjustment speed. In addition, the study establishes a link between price adjustment speed and profit.

The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.

A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

This study aims to investigate the dynamic motion of an ultrasonic machining system comprising two Duffing oscillators, each with a single degree of freedom. After derivation of the differential equations of the system using the Lagrange equations and dimensionless time, numerical analysis was used to observe changes in the system caused by differences in excitation frequency.

To suppress this effect and improve performance, proportional differential (PD) control was used. The integral absolute error was used as the fitness function, and particle swarm optimization was used to find the best value for the gain constant of the PD controller.

The results showed that with specific changes of excitation frequency, the dynamic motion of the system became nonlinear and chaotic behavior resulted. This made the system unstable and affected performance.

A range of methods, including fuzzy control, was used to analyze the results, and exhaustive laboratory work was carried out. Means of control were found that were effective in suppressing the chaotic behavior, and differences in response to control were investigated and verified. The findings of this study can be used as a basis for system parameter settings or control circuit design.

This paper aims to study the oscillation phenomenon before chaos as well as its mechanism of occurrence in the energy-saving and emission-reduction system.

The system dynamics analysis, phase portrait analyses, equilibrium point analysis and bifurcation curve were applied to this paper.

First, the authors find an oscillation phenomenon previous to chaos. Second, on the one hand, the existence of two unstable saddles is the reason for the occurrence of oscillation phenomenon. On the other hand, the increasing of carbon emissions can arouse oscillation phenomenon.

This paper finds an oscillation phenomenon previous to chaos in the energy-saving and emission-reduction system. The mechanism of occurrence of oscillation phenomenon is studied. The existence of two unstable saddles is the reason for the occurrence of such oscillation phenomenon. The oscillation is related with fold bifurcation. The study also provides a theoretical basis for the further study of chaos control.

The purpose of this paper is to investigate the chaotic dynamics behaviours and chaos control of differentiated Bertrand model.

The paper analyzes a nonlinear differentiated Bertrand duopoly game by using the theory of bifurcations of dynamical system, where players have heterogeneous expectations and nonlinear cost function: two types of players are considered – bounded rational and naive expectation. The equilibrium point and local stability of the duopoly game are investigated.

The paper demonstrates that as some parameters of the game are varied, the stability of Nash equilibrium is lost through period doubling bifurcation. The chaotic features are justified numerically via computing Lyapunov exponents, and sensitive dependence on initial conditions. By using the delay feedback control method, the authors have made the system form chaotic state to stable state.

This paper fulfils an identified need to study the diversity of expectations and how to lead to rich dynamics and complexity.

The scientific world has for a long time worked with linear tools to explain complex non‐linear phenomena. Also non‐linear relationships were transformed to linear in order to be handled. This was so despite the fact that nature has been giving us examples showing that the real world was complex, dynamic and non‐linear. This was so until developments in computer science provided the calculating means to the theory of complexity. Today, the theory of complexity is applied to many sciences and to disaster management as well. The application of complexity theory is attempted from a disaster management point of view. As the first attempt to incorporate management science into marine disaster prevention was the so‐called International Safety Management Code of the International Maritime Organization in 1998, we will attempt to connect the theory of complexity to the ISM code. The ISM code, being a safety standard, has been based on good management and organization rulesl. However, ISM code was accused of increasing the bureaucracy of the system with a result that no substance work could be done at the end. Moreover, a need has now emerged, i.e. to establish a “particular ISM code man” among the crewmen on board all ships. On the other hand, modern complexity management suggests more flat hierarchies where information travels faster, and this is something needed in a marine disaster.