This paper is concerned with 2-D discrete systems of the form x m + 1 , n = f ( x m , n , x m , n + 1 ) , where f : R 2 → R is a function, m, n ∈ N 0 ={0,1,2,…}. Some sufficient conditions for this system to be stable and a verification of this system to be chaotic in the sense of Devaney, respectively, are derived.
Dynamical behaviors of a new chaotic attractor is investigated in this paper. Some basic properties, bifurcations, routes to chaos, and periodic windows of the new system are studied either analytically or numerically. Meanwhile, the transition between the Lorenz attractor and Chen's attractor through the new system is explored.
Recounts Leon Chua's discovery of the memristor and the example Chua set for younger generations of scientists and engineers.
In this paper, the approach of the Karhunen–Loève decomposition, known also as the proper orthogonal modes (POMs), is taken to analyze phase synchronization of various complex networks with different topologies, namely the classic Kuramoto model, coupled chaotic maps with Gaussian delays and a chain of diffusively coupled bistable oscillators. In the case of the Kuramoto model, the POMs reveal the tendency and the level of synchronization with the increase of the coupling strength for globally coupled networks and scale-free networks, while periodic POMs are found in nearest-neighbor coupled networks. Furthermore, for cluster networks on the Kuramoto model, the first leading POMs based on different time intervals reveal that different sub-groups of nodes synchronize gradually to different levels, eventually leading to the complete phase synchronization. In the case of coupled chaotic maps, some properties of phase synchronization change with the coupling strength value. In the case of the chain of diffusively coupled bistable oscillators, several main POMs not only determine the network phase synchronization but also provide good reconstruction of the network responses.
We propose an approach to constructing different coupling schemes to stabilize selected cluster synchronization patterns for coupled Josephson equations. In particular, we select a coupling scheme to create synchronization with frequency ratio m 1 : m 2 : ⋯ : m n , which can be arbitrarily chosen and is independent of the frequencies of the uncoupled oscillators. We also discuss coupled discrete systems.
The purpose of this paper is to study the DC brush motor used in automobile engines. In the research, the diesel generator starting motor of the 4-pole 21-slot internal structure is used as the reference object prototype. The finite element magnetic circuit analysis software, RMxprt and Maxwell 2D by ANSYS, are used to modeling and analyze the transient magnetic field characteristics in a parametric manner. The electrical and magnetic characteristics including induced electromotive force, armature current, electromagnetic torque, rated speed, magnetic flux density and magnetic field distribution of the magnetic circuit are discussed. With the geometric dimensions of the reference motor, different stator and rotor core materials, the finite element analysis software RMxprt is used to quickly establish a DC brushed motor model. The results of the RMxprt were analyzed by two-dimensional finite element analysis software Maxwell 2D. Two improvement schemes are proposed to optimize the pole core. One is to cut the pole core into two parts, using different materials as the pole core, which can reduce the magnetic saturation phenomenon at the tip of the pole core. The second way is digging holes in the front pole tip forced the magnetic distribution toward to the rear pole tip for improving the magnetic saturation phenomenon. In the paper, the optimal design of the hole in the front pole of the pole core was selected. The stator structure was optimized by the Taguchi algorithm for maximum output power. At the rated speed of 3,400 rpm, the output torque after the reducer was 73.44 N-m, the output power can be as high as 7.69 kW, verified the feasibility of the improvement strategy.
In this paper, we introduce a model to describe knowledge accumulation through knowledge diffusion and knowledge upgrade in a multi-agent network. Here, knowledge diffusion refers to the distribution of existing knowledge in the network, while knowledge upgrade means the discovery of new knowledge. It is found that the population of the network and the number of each agent’s neighbors affect the speed of knowledge accumulation. Four different policies for updating the neighboring agents are thus proposed, and their influence on the speed of knowledge accumulation and the topology evolution of the network are also studied.
This brief addresses in a unified framework both global robust stability and synchronization problems for a class of directed networks with Lorenz-type nodes. When the key parameter in the node equation is modified, it covers the Lorenz, Chen, and Lu types of networks as special cases. Based on an observation about some special nonlinear characteristics of Lorenz-type systems, simple conditions are derived for global stability and synchronization of such networks, where the typical Lipschitz-type condition for nonlinear functions is not needed. By combining the pinning control strategy and a new linear control law, synchronization of a network with different nodes can be achieved. Several examples are given for illustration.
Network controllability refers to the ability of a networked system to drive its state to any desired configuration through control inputs. Controllability robustness ensures that this capability is maintained or retained under structural variations, such as node or edge failures caused by malicious attacks or random perturbations, which is critically important for real-world networks. This paper reviews existing metrics, evaluation methods and optimization strategies for controllability robustness, introducing also modeling techniques for attack processes. Analytical techniques, empirical simulations and machine learning-based approaches are presented, highlighting their respective advantages and limitations. Finally, some future directions are briefly discussed in four key areas: metrics design, evaluation refinement, optimization algorithms, and attack process modeling. By addressing these challenges, it is expected to develop more robust and stronger resilient networked systems.
We consider the problem of network security for distributed filtering under false data injection attacks over a wireless sensor network. To resist the hostile attacks from a malicious attacker who can inject false data into communication channels according to a certain probability, we design a protector for each sensor based on the online innovation information from its neighboring sensors to decide whether to use the received data at each time. To guarantee the Gaussianity of the innovations, we use a stochastic rule to transform the threshold detection. We also provide a sufficient condition for the stability of the estimator equipped with the proposed protector under hostile attacks. Moreover, we find a critical attack probability above which the steady-state estimation error covariance will exceed a pre-set value. Finally, we compare the estimation performances among several protection strategies, and explore the relationship between the system parameters and the protection effect.
It is important to present global non-linearized approximate method when the studies of nonlinear dynamical systems have been entering dominated fields.Seven different non-linearized approximate systems were given for a class of typical Hamiltonian system according to the different cases of two or three interaction points of equating potential lines.The approximate solutions(orbits)were given by integrating the corresponding approximate systems.It shows that the approximate elliptic periodic orbits can be obtained by the corresponding linearized systems and that the homoclinic(or heteroclinic) orbits can be obtained by the corresponding non-linearized systems with two or three order nonlinearities.Finally,the approximate methods are applied to analyze a concrete Hamiltonian system.
In this Rapid Communication, a switching manifold approach is proposed for synchronizing chaos. The effectiveness of this nonlinear control strategy is demonstrated by both theoretical analysis and numerical simulations on two typical chaotic systems: the Lorenz and the modified Lorenz systems.
