This paper introduces a new practical method for distinguishing chaotic, periodic and quasi-periodic orbits based on a new criterion, and apply it to investigate the local bifurcations of the Chen system. Conditions for supercritical and subcritical bifurcations are obtained, with their parameter domains specified. The analytic results are also verified by numerical simulation studies.
This paper establishes some equivalent conditions of a uninorm, extending an arbitrary triangular norm on [0, e] or an arbitrary triangular conorm on [e, 1] to the whole lattice.
No abstract is provided for this article.
A class of planar diffeomorphims is formulated, with infinitely many coexisting Smale horseshoes, where the Lebesgue measure of the parameters with such strange dynamics is infinite. On each horseshoe, there exists a uniformly hyperbolic invariant set, on which the map is topologically conjugate to the two-sided full-shift on two symbols. Moreover, the topological entropy is infinite in certain parameter regions.
Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback method is developed in this paper for Hopf bifurcation control for continuous-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 method and verify the theoretical results.
No abstract is provided for this article.
On the basis of pseudofractal networks (PFNs), we propose a family of delayed pseudofractal networks (DPFNs) with a special feature that newly added edges delay producing new nodes, differing from the evolution algorithms of PFNs where all existing edges simultaneously generate new nodes. We obtain analytical formulae for degree distribution, clustering coefficient (C) and average path length (APL). We compare DPFNs and PFNs, and show that the exponent of the degree distribution of DPFNs is smaller than that of PFNs, meaning that the heterogeneity of this kind of delayed network is higher. Compared to PFNs, small-world features of DPFNs are more prominent (larger C and smaller APL). We also find that the delay strengthens the scale-free and small-world characteristics of DPFNs. In addition, we calculate and compare the mean first passage time (MFPT) numerically, revealing that the MFPT of DPFNs is shorter. Our study may help with a deeper understanding of various deterministically growing delayed networks.
We study the effects of free will and massive opinion of multi-agents in a majority rule model wherein the competition of the two types of opinions is taken into account. To address this issue, we consider two specific models (model I and model II) involving different opinion-updating dynamics. During the opinion-updating process, the agents either interact with their neighbors under a majority rule with probability $1-q$, or make their own decisions with free will (model I) or according to the massive opinion (model II) with probability $q$. We investigate the difference of the average numbers of the two opinions as a function of $q$ in the steady state. We find that the location of the order-disorder phase transition point may be shifted according to the involved dynamics, giving rise to either smooth or harsh conditions to achieve an ordered state. For the practical case with a finite population size, we conclude that there always exists a threshold for $q$ below which a full consensus phase emerges. Our analytical estimations are in good agreement with simulation results.
In this paper, through numerical studies, we explore a new methodology for chaos synchronization via a hybrid (generalized plus identical) synchronization. An arbitrary signal, generated by an unknown dynamical system, can be synchronized by the hybrid chaotic system. The signal can then be stored for future application such as password and message identification. Each finite-length signal can, in principle, be labelled and stored by a unique number, provided that the key hybrid system parameter used for the purpose is suitably chosen within a one-to-one mapping range. The new methodology enables us to encode an arbitrary signal accurately and efficiently. Sufficient numerical simulations are shown to verify the proposed design. Potential applications of the developed hybrid chaos synchronization system include information storage, message identification, and certain types of secure signal and image communication.
In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: (1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology; (2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; (3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient.
This paper establishes several criteria for strong Li–Yorke chaos and distributional chaos in non-autonomous discrete dynamical systems. The main criterion of distributional δ-chaos for some δ>0 is induced by weak A-coupled-expansion in a sequence of nonempty compact subsets, where A is an irreducible transition matrix with at least one row sum larger than 1. Some of these results not only extend the existing related results for autonomous discrete systems to non-autonomous discrete systems, but also relax the assumptions of the counterparts. One example of a non-autonomous logistic system is provided for illustration.
In this paper, a multi‐consensus problem for networked multi‐agent systems in a weighted and directed graph with a nonlinear protocol is investigated. By using convergence theory, matrix theory and the method of Lyapunov functions, a sufficient condition for the networked multi‐agent systems to achieve multi‐consensus is derived. And the agreement of each group is studied. A feedback controller for the networked multi‐agent systems is then designed to drive the system to achieve multi‐consensus. Numerical simulations illustrate the effectiveness of the theoretical results.
