Stability and synchronous characteristics of a two exciters vibration system considering material motion

Nowadays, two exciters vibration system played an indispensable role in a majority of machinery and devices, such as vibratory feeder, vibrating screen, vibration conveyer, vibrating crusher, and so on. The stability of the system and the synchronous characteristics of two exciters are affected by material motion. However, those effects of material on two exciters vibration system were studied very little. Based on the special background, a mechanical model that two exciters vibration system considering material motion is proposed. Firstly, the system's dynamic equations are solved by using Lagrange principle and Newton's second law. Then, the motion stability of the system when material with different mass move on the vibrating body is analyzed by [Formula: see text] mapping and numerical simulation methods, and the motion forms of the material are also studied. Meanwhile, the frequency responses of the vibrating body are analyzed. Finally, the influence of material on the phase difference of the two exciters is revealed. It can be concluded that with the mass ratio of the material to the vibrating body increasing, the system's motion evolves from stable periodic motion to chaotic state, the synchronization ability of two exciters decline, and the unpredictability of abrupt change about the phase difference increases. Further, the uncertainties of both the abrupt change of phase difference and the collision location affect each other and eventually lead to the instability of the system.

The Complex Dynamics of Sharing Platform Competition Game

With the rapid development of Internet technologies and online sharing platforms, sharing economy has become a major trend in economy. The entry of sharing economy leads to profound impacts on incumbent industry. We build a dynamic sharing platform competition model with which agents are bounded rational, and consumer side is heterogeneous. Then, we present the fixed points and the stability conditions of the bifurcation of the dynamic model. We simulate the adjustment speed of sharing platform, sharing platform price, and costs of traditional firm effects on system stability, and we present stable area, bifurcation diagram, the largest Lyapunov exponent, and strange attractor of different parameters, and we give a feedback control method at last. Our main results are as follows: (1) when adjustment speed of sharing platform increases, the system becomes bifurcation, and finally, the system goes into a chaotic state; when the system is stable, price of traditional firm and fee decision of sharing platform are constant. (2) When price of sharing platform increases, sharing platform is more stable while traditional firm is more vulnerable. Suppose the system is in the stable state; when sharing platform price increases, traditional firm price increases, while sharing platform fees decreases. (3) When traditional firm cost is small, the system would be more stable. When the system is stable, with traditional firm cost increasing, traditional firm price increases quicker than sharing platform consumer fee, while sharing platform seller fee decreases. (4) Feedback control can alleviate the chaotic state of system. With feedback control parameter increases, the system becomes more stable.

Instability of holographic superfluids in optical lattice

The instability of superfluids in optical lattice has been investigated using the holographic model. The static and steady flow solutions are numerically obtained from the static equations of motion and the solutions are described as Bloch waves with different Bloch wave vector k. Based on these Bloch waves, the instability is investigated at two levels. At the linear perturbation level, we show that there is a critical kc above which the superflow is unstable. At the fully nonlinear level, the intermediate state and final state of unstable superflow are identified through numerical simulation of the full equations of motion. The results show that during the time evolution, the unstable superflow will undergo a chaotic state with soliton generation. The system will settle down to a stable state with k < kc eventually, with a smaller current and a larger condensate.

Comparative analysis of dynamic state recognition between permutation entropy and weighted permutation entropy

Permutation entropy (PE) and weighted permutation entropy (WPE) are indexes of the complex system. In this paper, the nonlinear sequence of two chaotic states is simulated by Logistic mapping, and the effectiveness of the PE and WPE algorithms in chaotic state recognition is compared and analyzed with different sliding step sizes. The results show that the value of WPE changes more obviously than PE in different chaotic states, and the recognition effect of WPE is better than PE in dynamic states, which can provide theoretical support for further analyzing the complexity characteristics of actual data.

Russia, the 1990s: Metamorphoses of the Emerging Polity

The article attempts to examine the era of the 1990s through the prism of communication in the system “center — regions”. The author interprets the epoch itself as a special, chaotic state of affairs. The political structures and instruments inherited by the new Russia from the Soviet times did not disappear, but lost their foundation (which corresponded to the model of Russian power described by Yuri Pivovarov), transformed into the mode of an autonomous drift along unauthorized trajectories. The new foundation (“the path of civilized countries”) came into conflict with the structures and instruments themselves. The situation was exacerbated by the fact that the rejection of that foundation deprived the political center of its legitimacy, since it was perceived and legitimized as a driver of the transition from socialism into the world of “civilized countries”. The article shows that it was the space of dialogue (bargaining) between the center and the regions that combined the principles of the Russian power and a new legitimizing foundation stemming from the “civilized countries” The author identifies three stages of such a dialogue. During the first stage, there was no adaptation, and the dialogue ended with a violent confrontation. As a result, two parallel realities emerged — the reality of legal norms and declarations and the reality of survival. The second stage, labeled by the author as “taming Europe”, witnessed democratic procedures uniting with the practices of the Russian power and recreation of the distributive economy at the regional level. At the same time, the dual legitimacy of the regional rulers — from the regional community and from the federal center — bound the country’s territory much stronger than enforcement agencies or future “spiritual staples”. The last stage, which is usually considered to take place after the 1990s, is associated with the transfer of practices that have developed in the regions to the center. However, according to the author’s conclusion, this is not the end of the constituent era and the formation of the polity, but a continuation of the quest.

Complex Dynamics Analysis of Closed-Loop Supply Chain considering CSR and Fairness Concerns

This paper constructs a supply chain model composed of a manufacturer and a recycler. The manufacturer’s CSR and the recycler’s fairness concerns are introduced to the benchmark model in turn, and the optimal decision-making problems under different models are studied and compared. The findings show that the manufacturer’s utility will increase and the recycler’s utility will decrease when the manufacturer undertakes CSR within a reasonable range. The optimal utility of manufacturers does not change, and the utility of the recycler is affected by the proportion of CSR undertaken by the manufacturer when the recycler considers fairness concerns. Based on the CSR and fairness model, this paper constructs a dynamic decision system of production quantity and eco-innovation effort. We analyze the influence of adjustment speed on the dynamic decision system and obtain the conditions required to maintain system stability. The research conclusion indicates that with the increase of adjusting parameters, the system gradually appears chaotic state from a stable state and the chaotic state of the system has a negative impact on the utility of manufacturer and recycler. In order to avoid chaos in the system, this paper uses the delayed feedback method to control the system.

Astrocytic Based Controller Shifts Epileptic Activity to the Chaotic State

Investigating effective controller to shift hippocampal epileptic periodicity to normal chaotic behavior will be new hope for epilepsy treatment. Astrocytes nourish and protect neurons as well as maintaining synaptic transmission and network activity. Therefore, this study explores the ameliorating effect of astrocyte computational model on epileptic periodicity. Modified Morris-Lecar equations were used to model hippocampal CA3 network. Network inhibitory parameters were employed to generate oscillation induced epileptiform periodicity. The astrocyte controller was based on a functional dynamic mathematical model of brain astrocytic cells. Results demonstrated that synchronization of two neural networks shifted the brain chaotic state to periodicity. Applying astrocytic controller to the synchronized networks returned the system to the desynchronized chaotic state. It is concluded that astrocytes are probably a good model in controlling epileptic periodicity. However, more research efforts are needed to delineate the effect.

Controlling chaos by the system size

Despite the ubiquity of physical systems evolving on time-dependent spatial domains, understanding their regular and chaotic dynamics is still in a rudimentary state. While chaos implies that the system’s behavior can be altered by small perturbations, this sensitivity proves to be useful for control purposes. Here we report on the experimental discovery of a novel mechanism to control chaos by time-variation of the system (spatial domain) size: depending upon the rate of the latter, the chaotic state may be completely prevented. Our experimental observations are disentangled with theoretical insights and numerical modeling, which also reveals the ability to control spatio-temporal chaos, thus making the findings relevant to a wide range of natural phenomena.

Dynamic behavior of fractional-order memristive time-delay system and image encryption application

This paper presents dynamic behavior of a fractional-order memristive time-delay system and its application in image encryption. First, a fractional-order memristive time-delay system is proposed, and the stability and bifurcation behaviors of the system are theoretically analyzed. Some limited conditions for describing the stability interval and switching between different dynamic behaviors are derived. Second, the dynamic characteristics of the system are analyzed through the coexisting attractors, coexisting bifurcation diagrams, the Largest Lyapunov exponents (LLE), the 0-1 test. When parameters change, such as time delay and fractional order, the system transits from steady state to periodic state, single scroll chaotic state, double scroll chaotic state. Furthermore, an image encryption scheme based on the fractional-order memristive time-delay system is introduced, and some statistical features are analyzed. Finally, numerical simulations verify the validity of the theoretical analysis and safety of the image encryption scheme based on the fractional-order delayed memristive chaotic system.