Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique

This paper develops some new Razumikhin-type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations. Compared with some existing works, a distinctive feature of this paper is to address exponential stability problems for any finite delay. It is shown that the functional differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. Two examples verify the effectiveness of the proposed results

A heterozygous moth genome provides insights into herbivory and detoxification

How an insect evolves to become a successful herbivore is of profound biological and practical importance. Herbivores are often adapted to feed on a specific group of evolutionarily and biochemically related host plants1, but the genetic and molecular bases for adaptation to plant defense compounds remain poorly understood2. We report the first whole-genome sequence of a basal lepidopteran species, Plutella xylostella, which contains 18,071 protein-coding and 1,412 unique genes with an expansion of gene families associated with perception and the detoxification of plant defense compounds. A recent expansion of retrotransposons near detoxification-related genes and a wider system used in the metabolism of plant defense compounds are shown to also be involved in the development of insecticide resistance. This work shows the genetic and molecular bases for the evolutionary success of this worldwide herbivore and offers wider insights into insect adaptation to plant feeding, as well as opening avenues for more sustainable pest management.Minsheng You … Simon W Baxter … et al

Exponential Consensus of Multi-Agent Systems under Event-Triggered Impulsive Control with Actuation Delays

This paper investigates the exponential consensus problem for a class of nonlinear leader-following multi-agent systems using impulsive control, where impulses are generated by the event-triggered mechanism and are subjected to actuation delays. It is proved that Zeno behavior can be avoided, and by employing the linear matrix inequality technique, some sufficient conditions for realizing exponential consensus of the considered system are derived. Actuation delay is an important factor affecting the consensus of the system, and our results show that increasing the actuation delay can enlarge the lower bound of the triggering interval, while it harms the consensus. To demonstrate the validity of the obtained results, a numerical example is provided

Some criteria on pth moment stability of impulsive stochastic functional differential equations

By using Lyapunov-Razumikhin method, some criteria on pth moment stability and pth moment asymptotical stability of impulsive stochastic functional differential equations are obtained. An example is also presented to illustrate the efficiency of our results.Impulsive stochastic functional differential equations pth moment stability pth moment asymptotic stability Razumikhin-type technique

Finite‐time consensus of leader‐following non‐linear multi‐agent systems via event‐triggered impulsive control

Abstract This work is concerned with the finite‐time consensus of leader‐following non‐linear multi‐agent systems by means of distributed event‐triggered impulsive control. The finite‐time consensus protocol is first put forward based on event‐triggered impulsive strategies, where the impulsive instants are determined by the proposed event‐triggered condition. For the event‐triggered condition, it not only determines the impulsive instants but also effects the update time of the finite‐time control. Moreover, compared with the existing finite‐time controllers, the controller designed in this work does not contain any sign function, thereby overcoming the chattering phenomenon. In addition, without finding Zeno behaviour, the feasibility of the proposed control protocol is demonstrated. Lastly, simulations are employed to demonstrate the effectiveness of the proposed control schemes

Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems

Quasi-Consensus of Time-Varying Multi-Agent Systems with External Inputs under Deception Attacks

The quasi-consensus of a class of nonlinear time-varying multi-agent systems suffering from both external inputs and deception attacks is studied in this paper. This is different from a time-varying matrix, which is assumed to be bounded; further reasonable assumptions are supposed. In addition, impulsive deception attacks modeled with Bernoulli variables are considered. Sufficient conditions to achieve quasi-consensus are given, and the upper bounds of the error state related to the deception attacks is derived. Finally, a numerical simulation example is provided to show the validity of the obtained results