An Improved Intrusion Weed Optimization Algorithm for Node Location in Wireless Sensor Networks

The distribution optimization of WSN nodes is one of the key issues in WSN research, and also is a research hotspot in the field of communication. Aiming at the distribution optimization of WSN nodes, the distribution optimization scheme of nodes based on improved invasive weed optimization algorithm(IIWO) is proposed. IIWO improves the update strategy of the initial position of weeds by using cubic mapping chaotic operator, and uses the Gauss mutation operator to increase the diversity of the population. The simulation results show that the algorithm proposed in this paper has a higher solution quality and faster convergence speed than IWO and CPSO. In distribution optimization example of WSN nodes, the optimal network coverage rate obtained by IIWO is respectively improved by 1.82% and 0.93% than the IWO and CPSO. Under the condition of obtaining the same network coverage rate, the number of nodes required by IIWO is fewer.

Characteristics of (α,β)-Mean Li–Yorke Chaos of Linear Operators on Banach Spaces

In this paper, we introduce a new concept, [Formula: see text]-mean Li–Yorke chaotic operator, which includes the standard mean Li–Yorke chaotic operators as special cases. We show that when [Formula: see text] or [Formula: see text], [Formula: see text]-mean Li–Yorke chaotic dynamics is strictly stronger than the ones that appeared in mean Li–Yorke chaos. When [Formula: see text] or [Formula: see text], it has completely different characteristics from the mean Li–Yorke chaos. We prove that no finite-dimensional Banach space can support [Formula: see text]-mean Li–Yorke chaotic operators. Moreover, we show that an operator is [Formula: see text]-mean Li–Yorke chaos if and only if there exists an [Formula: see text]-mean semi-irregular vector for the underlying operator, and if and only if there exists an [Formula: see text]-mean irregular vector when [Formula: see text], which generalizes the recent results by Bernardes et al. given in 2018. When [Formula: see text], we construct a counterexample in which it is an [Formula: see text]-mean Li–Yorke chaotic operator but does not admit an [Formula: see text]-mean irregular vector. In addition, we show that an operator with dense generalized kernel is [Formula: see text]-mean Li–Yorke chaotic if and only if there exists a residual set of [Formula: see text]-mean irregular vectors, and if and only if there exists an [Formula: see text]-mean unbounded orbit.

Chaos and frequent hypercyclicity for composition operators

The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Ruzsa in 2015 that for backward weighted shifts on $\ell _p(\mathbb {Z})$ , the notions of chaos and frequent hypercyclicity coincide. It is with some effort that one shows that these two notions are distinct. Bayart and Grivaux in 2007 constructed a non-chaotic frequently hypercyclic weighted shift on $c_0$ . It was only in 2017 that Menet settled negatively whether every chaotic operator is frequently hypercylic. In this article, we show that for a large class of composition operators on $L^{p}$ -spaces, the notions of chaos and frequent hypercyclicity coincide. Moreover, in this particular class, an invertible operator is frequently hypercyclic if and only if its inverse is frequently hypercyclic. This is in contrast to a very recent result of Menet where an invertible operator frequently hypercyclic on $\ell _1$ whose inverse is not frequently hypercyclic is constructed.

Clone Chaotic Parallel Evolutionary Algorithm for Low-Energy Clustering in High-Density Wireless Sensor Networks

Because the sensors are constrained in energy capabilities, low-energy clustering has become a challenging problem in high-density wireless sensor networks (HDWSNs). Usually, sensor nodes tend to be tiny devices along with constrained clustering abilities. To have a low communication energy consumption, a low-energy clustering scheme should be designed properly. In this work, a new cloned chaotic parallel evolution algorithm (CCPEA) is proposed, and a low-energy clustering model is established to lower the communication energy consumption of HDWSNs. By introducing CCPEA into the low-energy clustering, an objective function is designed for evaluating the communication energy consumption. For this problem, we define a clone operator to minimize the communication energy consumption of HDWSNs, use the chaotic operator to randomly generate the initial population to expand the search range to avoid local optimization, and find the parallel operator to speed up the convergence speed. In the experiment, the effect of CCPEA is compared to heuristic approaches of particle swarm optimization (PSO) and simulated annealing (SA) for the HDWSNs with different numbers of sensors. Simulation experiments demonstrate that the presented CCPEA method achieves a lower communication energy consumption and faster convergence speed than PSO and SA.

On Subspace-recurrent Operators

In this article, subspace-recurrent operators are presented and it is showed that the set of subspace-transitive operators is a strict subset of the set of subspace-recurrent operators. We demonstrate that despite subspace-transitive operators and subspace-hypercyclic operators, subspace-recurrent operators exist on finite dimensional spaces. We establish that operators that have a dense set of periodic points are subspace-recurrent. Especially, if $T$ is an invertible chaotic or an invertible subspace-chaotic operator, then $T^{n}$, $T^{-n}$ and $\lambda T$ are subspace-recurrent for any positive integer $n$ and any scalar $\lambda$ with absolute value $1$. Also, we state a subspace-recurrence criterion.

Dynamical Model Identification for a Small-Scale Unmanned Helicopter Using an Integrated Approach

This article presents an integrated approach for the parameter identification of a small-scale unmanned helicopter. With the flight experiment data collection and preprocessing, a hybrid identified algorithm combining the improved artificial bee colony algorithm and prediction error method is proposed to obtain the unknown dynamical parameters of the linear model. The proposed algorithm is valid to use thanks to an adaptive search equation, a novel probability-scaling method, and a chaotic operator and has a good performance in search speed and quality. Afterwards, we design a wind tunnel test to modify the main rotor time constant of the identified model. The identified accuracy and feasibility of the proposed approach are verified by making a time-domain comparison with three other algorithms. Results show that the dynamical characteristics of the helicopter can be determined accurately by the identified model. And the proposed approach is propitious to enhance the reliability and availability of the identified dynamical model.

Chaotic backward shift operator on Chebyshev polynomials

We obtain the representation of the backward shift operator on Chebyshev polynomials involving a principal value (PV) integral. Twice the backward shift on the space of square-summable sequences l2 displays chaotic dynamics, thus we provide an explicit form of a chaotic operator on L2 (−1, 1, (1−x2)–1/2) using Cauchy’s PV integral. We explicitly calculate the periodic points of the operator and provide examples of unbounded trajectories, as well as chaotic ones. Histograms and recurrence plots of shifts of random Chebyshev expansions display interesting behaviour over fractal measures.

Nonlinear Friction and Dynamical Identification for a Robot Manipulator with Improved Cuckoo Search Algorithm

This paper concerns the problem of dynamical identification for an industrial robot manipulator and presents an identification procedure based on an improved cuckoo search algorithm. Firstly, a dynamical model of a 6-DOF industrial serial robot has been derived. And a nonlinear friction model is added to describe the friction characteristic at motion reversal. Secondly, we use a cuckoo search algorithm to identify the unknown parameters. To enhance the performance of the original algorithm, both chaotic operator and emotion operator are employed to help the algorithm jump out of local optimum. Then, the proposed algorithm has been implemented on the first three joints of the ER-16 robot manipulator through an identification experiment. The results show that (1) the proposed algorithm has higher identification accuracy over the cuckoo search algorithm or particle swarm optimization algorithm and (2) compared to linear friction model the nonlinear model can describe the friction characteristic of joints better.