Synchronization in Dynamically Coupled Fractional-Order Chaotic Systems: Studying the Effects of Fractional Derivatives

This study presents the effectiveness of dynamic coupling as a synchronization strategy for fractional chaotic systems. Using an auxiliary system as a link between the oscillators, we investigate the onset of synchronization in the coupled systems and we analytically determine the regions where both systems achieve complete synchronization. In the analysis, the integration order is considered as a key parameter affecting the onset of full synchronization, considering the stability conditions for fractional systems. The local stability of the synchronous solution is studied using the linearized error dynamics. Moreover, some statistical metrics such as the average synchronization error and Pearson’s correlation are used to numerically identify the synchronous behavior. Two particular examples are considered, namely, the fractional-order Rössler and Chua systems. By using bifurcation diagrams, it is also shown that the integration order has a strong influence not only on the onset of full synchronization but also on the individual dynamic behavior of the uncoupled systems.

THE CONCEPT OF THE CLUTCH CONTROL LAW OF A CAR

Problem. The combination of comfortable automatic control of the car's transmission and at the same time preservation of high indicators of energy efficiency and cost of a design is possible by use of automatic mechanical transmission. The automatic clutch control system plays a significant role in providing comfort in such transmissions. The laws of controlling it are not perfect today. Goal. The aim of the work is to create a clear concept of the law of clutch control, which is easy to implement in a microcontroller and is well adapted to adapt to different driving conditions. Methodology. Graphically, the concept of the perspective law of clutch control is formed by two Bezier curves. One of the curves acts as a guide, and the other forms the surface of the law. Results. On the basis of the Bézier curves of the third degree the concept of the law is formed and the connection of the reference points of the Bézier curves with the physical parameters of the working process of vehicle movement is substantiated. Originality. The formation of the Bézier curve, which is decisive for the concept of the law, is formed on the basis of a typical working process of synchronization of the angular velocity of the clutch discs during the movement of the vehicle. In contrast to the laws of clutch control considered in the scientific literature, the proposed concept provides for clutch control outside the site of the synchronization process and ensures the avoidance of jerks during further acceleration. Practical value. The proposed algorithm provides full engagement of the clutch only after full synchronization of the clutch discs. The formation of a special form of the law in the form of a curve tangent to the abscissa axis reduces the jerks when closing the clutch discs.

Pattern selection in multi-layer network with adaptive coupling

Feed-forward effect modulates collective behavior of a multiple neuron network and facilitates strongly synchronization of their firing in deep layers. However, full synchronization of neuron system corresponds to functional disorder. In this work, we investigate coexistence of synchronized and incoherent neurons in deeper layer (called chimera state) in order to avoid the contradiction between facilitation of full synchronization and complete functional failure of neuron system. We focus on a multiple network containing two layers and confirm that chimera state in layer 1 could also induce that in layer 2 when the feed-forward effect is strong enough. Cluster also is discovered as a transient state which separates full synchronization and chimera state and occupy a narrow region. Both feed-forward and back-forward effect together emerge of chimera states in both layer 1 and 2 under same parameter in large range of parameters selection. Further, we introduce adaptive dynamics into inter-layer rather than intra-layer couplings. Under this circumstance chimera state still can be induced and coupling matrix will be self-organized under suitable phase parameter to guarantee chimera formation. Indeed, chimera states exist and transit to deeper layer in a regular multiple network with very strict parameter selection. The results helps understanding better the neuron firing propagating and encoding scheme in a multi-layer neuron network.

Multistability of Globally Coupled Duffing Oscillators

We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized clusters, as a consequence of the bistability of individual oscillators. The multiplicity of these solutions, induced by the many possible ways of distributing the oscillators between the two clusters, implies that the ensemble can exhibit multistability. As the strength of coupling grows, however, the two-cluster solutions are replaced by a state of full synchronization. By a combination of analytical and numerical techniques, we study the existence and stability of two-cluster solutions. The role of the distribution of oscillators between the clusters and the relative prevalence of the two stable solutions are disclosed.

Grand-Expert spectrometer for metal analysis: current status and analytical capabilities

This paper presents the characteristics of the modern Grand-Expert spectrometer for the analysis of metals and alloys. The spectrometer has an updated optical scheme and a new spectrum analyzer to solve a wide range of analytical tasks. The analytical capabilities of the spectrometer were investigated for the analysis of steels and high-purity copper and aluminum as an example. For each of the bases, the updated optical scheme made it possible to realize new opportunities for controlling the homogeneity of the sample material and the presence of micro-inclusions on the sample surface and for determining low impurity contents in the pure metal bases. The spectrometer uses a modern semiconductor spark generator with adjustable frequency, current intensity, and duration of individual spark pulses. Spectra of metal samples for individual spark pulses were obtained in real time for the investigated sample. The operation of the spectrometer in different modes and with different exposure times was tested to select the optimal parameters of calibration characteristics. Computer control provides full synchronization of the generator mode setting, argon feeding, and spectrum registration. For steels, we selected sparking modes with high stability of spectral line intensities and analyte concentrations, and for pure metals (copper and aluminum), modes providing low detection limits of impurity elements and good stability of the results.

An Improved Method to Evaluate the Synchronization in Neural Key Exchange Protocol

The synchronization between two neural networks by mutual learning can be used to design the neural key exchange protocol. The critical issue is how to evaluate the synchronization without a weight vector. All existing methods have a delay in evaluating the synchronization, which affects the security of the neural key exchange. To evaluate the full synchronization of neural networks more timely and accurately, an improved method for evaluating the synchronization is proposed. First, the frequency that the two networks have the same output in previous steps is used for assessing the degree of them roughly. Second, the hash function is utilized to judge whether the two networks have achieved full synchronization precisely when the degree exceeds a given threshold. The improved method can find the full synchronization between two networks with no information other than the hash value of the weight vector. Compared with other methods, the full synchronization can be detected earlier by two communication partners which adopt the method proposed in this paper. As a result, the successful probability of geometric is reduced. Therefore, the proposed method can enhance the security of the neural exchange protocol.

The conditions of full synchronization in generalized Kuramoto models [in Polish: Warunki pełnej synchronizacji w uogólnionych modelach Kuramoto]

A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and numerically that finite-size systems may have many different synchronized stable solutions which are characterised by different values of the winding number. The lower bound for the critical coupling $k_c$ is given, as well as an algorithm for its exact calculation. It is shown that in general phase-locking does not lead to phase coherence in 1D.

CikA, an Input Pathway Component, Senses the Oxidized Quinone Signal to Generate Phase Delays in the Cyanobacterial Circadian Clock

The circadian clock is a timekeeping system in most organisms that keeps track of the time of day. The rhythm generated by the circadian oscillator must be constantly synchronized with the environmental day/night cycle to make the timekeeping system truly advantageous. In the cyanobacterial circadian clock, quinone is a biological signaling molecule used for entraining and fine-tuning the oscillator, a process in which the external signals are transduced into biological metabolites that adjust the phase of the circadian oscillation. Among the clock proteins, the pseudo-receiver domain of KaiA and CikA can sense external cues by detecting the oxidation state of quinone, a metabolite that reflects the light/dark cycle, although the molecular mechanism is not fully understood. Here, we show the antagonistic phase shifts produced by the quinone sensing of KaiA and CikA. We introduced a new cyanobacterial circadian clock mixture that includes an input component in vitro. KaiA and CikA cause phase advances and delays, respectively, in this circadian clock mixture in response to the quinone signal. In the entrainment process, oxidized quinone modulates the functions of KaiA and CikA, which dominate alternatively at day and night in the cell. This in turn changes the phosphorylation state of KaiC—the central oscillator in cyanobacteria—ensuring full synchronization of the circadian clock. Moreover, we reemphasize the mechanistic input functionality of CikA, contrary to other reports that focus only on its output action.

Programmable dynamic steady states in ATP-driven nonequilibrium DNA systems

Inspired by the dynamics of the dissipative self-assembly of microtubules, chemically fueled synthetic systems with transient lifetimes are emerging for nonequilibrium materials design. However, realizing programmable or even adaptive structural dynamics has proven challenging because it requires synchronization of energy uptake and dissipation events within true steady states, which remains difficult to orthogonally control in supramolecular systems. Here, we demonstrate full synchronization of both events by ATP-fueled activation and dynamization of covalent DNA bonds via an enzymatic reaction network of concurrent ligation and cleavage. Critically, the average bond ratio and the frequency of bond exchange are imprinted into the energy dissipation kinetics of the network and tunable through its constituents. We introduce temporally and structurally programmable dynamics by polymerization of transient, dynamic covalent DNA polymers with adaptive steady-state properties in dependence of ATP fuel and enzyme concentrations. This approach enables generic access to nonequilibrium soft matter systems with adaptive and programmable dynamics.

Programmable Dynamic Steady States in ATP-Driven Non-Equilibrium DNA Systems

<div><div><div><p>Inspired by the dynamics of the dissipative self-assembly of microtubules, chemically fueled synthetic systems with transient lifetimes are emerging for non-equilibrium materials design. However, realizing programmable or even adaptive structural dynamics has proven challenging because it requires synchronization of energy uptake and dissipation events within true steady states, which remains difficult to orthogonally control in supramolecular systems. Here, we demonstrate full synchronization of both events by ATP-fueled activation and dynamization of covalent DNA bonds via an enzymatic reaction network of concurrent ligation and cleavage. Critically, the average bond ratio and the frequency of bond exchange are imprinted into the energy dissipation kinetics of the network and tunable through its constituents. We introduce temporally and structurally programmable dynamics by polymerization of transient, dynamic covalent DNA polymers with adaptive steady-state properties in dependence of ATP fuel and enzyme concentrations. This approach enables generic access to non-equilibrium soft matter systems with adaptive and programmable dynamics.</p></div></div></div>