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Based on a method of network split through different nature of time-delay, this paper is further investigates the pinning synchronization of the directed complex dynamical networks with multi-links. Via the theory of Lyapunov stability combined with linear matrix inequalities(LMIs) technique and the method of the free-weighting matrix, some sufficient conditions for global synchronization by adding linear feedback controllers to a part of nodes are obtained. Numerical examples are also provided to demonstrate the effectiveness of the theory.

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The residence time distribution (RTD) curve is widely applied to describe the fluid flow in a tundish, different tracer mass concentrations and different tracer volumes give different residence time distribution curves for the same flow field. Thus, it is necessary to have a deep insight into the effects of the mass concentration and the volume of tracer solution on the residence time distribution curve. In order to describe the interaction between the tracer and the fluid, solute buoyancy is considered in the Navier–Stokes equation. Numerical results show that, with the increase of the mass concen-tration and the volume of the tracer, the shape of the residence time distribution curve changes from single flat peak to single sharp peak and then to double peaks. This change comes from the stratified flow of the tracer. Furthermore, the velocity difference number is introduced to demonstrate the importance of the density difference between the tracer and the fluid.

Recently, the physical limitation of range-domain security guarantee for directional modulation with frequency diverse array was disclosed in Ding et al. (IEEE Access 8, 63302-63309 (2020)). Therefore, to recreate this significant secrecy realisation in both direction and range domain, the authors conceive an artificial noise aided directional modulation scheme via reconfigurable intelligent surface. Specifically, the angle of departure from the reconfigurable intelligent surface to co-direction receivers varies with distance, which provides the freedom to distinguish users in the range domain. With locations of the active eavesdroppers, an optimisation problem is further formulated to maximise the secrecy rate, which is then solved by applying genetic algorithm and alternating optimisation. On the other hand, when the eavesdroppers are silent, we employ maximum-ratio transmission precoding and artificial noise to guarantee information security. Finally, simulation results demonstrate that, due to the aid of reconfigurable intelligent surface, the developed directional modulation structure can robustly guarantee the information security in the range domain, whether the information of eavesdroppers is achieved.

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To keep the resources renewable, a singular ecological-economic model is proposed for the populations with harvesting and migration. The local stability and the dynamic behavior of the model are studied. Singular induced bifurcation appears when economic interest is zero, which is different from the ordinary differential models. In order to apply variable structure control to eliminate these complex behaviors, the singular model is transformed into a single-input and single-output model with parameter varying within definite intervals. And then, a variable structure controller is designed to make the model stable. Finally, an inshore-offshore fishery model is given to illustrate the proposed method, and some numerical simulations are shown to demonstrate the control results.

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