This paper studies robust impulsive synchronization of uncertain dynamical networks. By utilizing the concept of im- pulsive control and the stability results for impulsive systems, sev- eral criteria for robust local and robust global impulsive synchro- nization are established for complex dynamical networks, in which the network coupling functions are unknown but bounded. Three examples are also worked through for illustrating the main results. Index Terms—Chaotic synchronization, globally robustly impul- sive synchronization, locally robust impulsive synchronization, net- work coupling, uncertain dynamical networks.
A single-input multiple-output (SIMO) architecture of the frequency-modulated (FM) differential code-shift keying (DCSK) modulation technique is proposed. The new scheme employs orthogonal Walsh functions at the transmitter, with parallel substreams transmitted with a single antenna to help achieve a significant increase of the data rate. Multiple antennas are used at the receiver end to form an SIMO structure so as to obtain a diversity gain. Simulation results demonstrate that at a higher signal-to-noise ratio, the proposed SIMO FM-DCSK architecture has an outstanding bit error rate performance, in contrast to the direct-sequence (DS) vertical Bell Labs layered space-time (VBLAST) scheme that uses a complicated Rake receiver and minimum mean-square error detection, at the same data rate over multipath fading channels. In particular, the new scheme does not require any prior knowledge of the channel states, exact synchronization, and the complex Rake receiver, making the proposed algorithm simpler and yet more efficient than the DS-VBLAST scheme.
All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
For a class of nonlinear diffusion–convection–reaction equations, the corresponding traveling wave systems are well-known nonlinear oscillation type of systems. Under some parameter conditions, the first integrals of these nonlinear oscillators can be obtained. In this paper, the bifurcations, exact solutions and dynamical behavior of these nonlinear oscillators are studied by using methods of dynamical systems. Under some parametric conditions, exact explicit parametric representations of the monotonic and nonmonotonic kink and anti-kink wave solutions, as well as limit cycles, are obtained. Most important and interestingly, a new global bifurcation phenomenon of limit bifurcation is found: as a key parameter is varied, so that singular points (except the origin) disappear, a planar dynamical system can create a stable limit cycle.
Many evolutionary processes, particularly some biological systems, exhibit impulsive dynamical behaviors, which can be well described by impulsive Hopfield neural networks. This paper formulates and studies a model of delayed impulsive Hopfield neural networks. Several fundamental issues such as global exponential stability, existence and uniqueness of the equilibrium of such networks are established. A numerical example is given for illustration and interpretation of the theoretical results.
Bifurcation control has attracted increasing attention in recent years. A simple and unified state‐feedback methodology is developed in this paper for Hopf bifurcation control for discrete‐time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.
This paper shows that there exists a contraction whose Zadeh's extension is not a contraction under the Skorokhod metric, answering negatively Problems 5.8 and 5.12 posted in Jardón, Sánchez, and Sanchis (2019) [5].
This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.
Δ-modulated feedback control of a linear system introduces nonlinearity into the system through switchings between two input values. It has been found that Δ-modulation gives rise to periodic orbits. The existence of periodic points of all orders of Sigma-Delta modulation with “leaky” integration is completely characterized by some interesting groups of polynomials with “sign” coefficients. The results are naturally generalized to Sigma-Delta modulations with multiple delays. Further extensions relate to the existence of periodic points arising from Δ-modulated feedback control of a stable linear system in an arbitrary direction, for which some necessary and sufficient conditions are given.
This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.
A unified chaotic system has recently been proposed such that different classes of chaotic systems, including Lorenz, Chen and Lü systems, can be re-generated by varying a single system parameter. In this paper, an electronic circuit is designed and built to confirm this new chaotic system. In our experiments, it is illustrated that different chaotic attractors can be duly obtained by controlling two switches in the circuit.
Epidemiological models with bilinear incidence rate usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable nontrivial equilibrium (i.e.interior equilibrium) corresponding to the endemic state.In this paper, we consider an epidemiological model, which is a SIRS (susceptible-infected-removed-susceptible) model influenced by random perturbations.We prove that the solutions of the system are positive for all positive initial conditions and that the solutions are global, that is, there is no finite explosion time.We present necessary and sufficient condition for the almost sure asymptotic stability of the steady state of the stochastic system.
