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• A normal form is derived for codimension-two focus-fold bifurcation. • Observations of focus-fold bifurcation are extended from piecewise linear systems to general piecewise smooth systems. • Two types of sliding limit cycles are bifurcated from the focus-fold singularity for general piecewise smooth systems. • Two nested crossing limit cycles are bifurcated from the focus-fold singularity for general piecewise smooth systems. • Convergence in finite time is proved for sliding limit cycles. We consider codimension-two focus-fold bifurcation for general piecewise smooth (PWS) planar systems. Some changes of variables and parameters are employed to derive a normal form, which is topologically equivalent to the original system. Making use of the normal form, we verify that observations of focus-fold bifurcation in some special piecewise linear systems also hold for general PWS systems, including the existence of two types of sliding limit cycles and coexistence of crossing and sliding limit cycles. It is shown that two nested crossing limit cycles can be bifurcated from the focus-fold singularity. This result is the improvement of the work [Han and Zhang (2010) [29] ], in which only one bifurcated limit cycle is obtained. In addition, the sliding limit cycles are proved to be convergent in finite time. [ABSTRACT FROM AUTHOR]

In this work, a new perturbation approach is developed based on Bogdanov-Takens bifurcation theory, which enables the Poincaré-Lyapunov method for switching systems with linear type centers to be applied for studying the center conditions of planar switching polynomial systems associated with a nilpotent equilibrium point. The new method is then applied to consider a class of quadratic switching nilpotent systems, and a complete classification is given on the conditions of the nilpotent equilibrium point to be a center. Moreover, based on one of the center conditions, an example is constructed to show the existence of seven small-amplitude limit cycles around the nilpotent equilibrium point, which is a new lower bound on the number of limit cycles in such systems. [ABSTRACT FROM AUTHOR]

Autophagy, an evolutional conserved lysosomal degradation process, has been implicated to play an important role in cellular defense against a variety of microbial infection. Interestingly, numerous studies found that some pathogens, especially positive-single-strand RNA viruses, actually hijacked autophagy machinery to promote virus infection within host cells, facilitating different stages of viral life cycle, from replication, assembly to egress. Enterovirus, a genus of positive-strand RNA virus, can cause various human diseases and is one of main public health threat globally, yet no effective clinical intervention is available for enterovirus infection. Here we summarized recent literature on how enteroviruses regulate and utilize autophagy process to facilitate their propagation in the host cells. The studies on the interplay between enterovirus and autophagy not only shed light on the molecular mechanisms underlying how enterovirus hijacks cellular components and pathway for its own benefits, but also provide therapeutic option against enterovirus infection. [ABSTRACT FROM AUTHOR]

In this paper, a Filippov ratio-dependent predator–prey model is proposed to describe the effect on behavioral refuges caused by prey instinct anti-predator behavior. The proposed model extends the classical ratio-dependent predator–prey model by combining a prey–predator ratio that describes the behavioral refuges make sense once it is less than a certain threshold. One of the prominent mathematical features of our model, distinguishing from the classical one, is that there exist singular points on discontinuous surface whose characteristics determine the main dynamical behaviors of this model. The complete analysis of topological structures of orbits near all the singular points is presented. We show 14 types of system behaviors realized for various parameter values. In particular, globally stable pseudo-equilibrium and globally finite time stable canard cycle are shown to exist in some ranges of parameter values, which cannot be achieved in classical model. [ABSTRACT FROM AUTHOR]

Cd pollution in farmland is becoming a serious problem because it affects the safety of rice production and human health. Salicylic acid (SA) plays crucial roles in plant development and mediates plant responses to biotic and abiotic stress. This study assessed the molecular and physiological mechanisms of SA spraying effects on Cd tolerance and Cd accumulation in rice. Spraying of 0.1 mM SA had no great effect on the agronomic traits of rice, but significantly decreased Cd accumulation in rice grains, and SA spraying increased the Cd contents in leaves (only at the mature stage) and decreased the Cd contents in panicles (only at the filling and mature stage), but had no evident impact on the Cd content of other tissues and other growth stages. SA spraying reduced Cd accumulation in rice grains by promoting the deposition and fixation of Cd in the cell wall of leaves, thus preventing Cd being transferred from leaves to rice grains at the filling stage. SA spraying also decreased Cd toxicity by reducing H 2 O 2 and MDA accumulation and increasing the chlorophyll content in rice leaves. Furthermore, SA spraying remarkably decreased Cd accumulation in rice grains by modulating the expression level of the genes associated with Cd translocation and accumulation to control the Cd accumulation in rice. Hence, SA spraying reduced the inhibition of Cd on the plant height caused by Cd and increased the dry weight of shoots in the vegetative growth period of rice seedlings, and it reduced Cd transport from leaves to grains, thus reducing Cd content in rice. These findings provide a novel perspective and a new method for reducing Cd accumulation in rice. Image 1 • SA spraying reduces Cd accumulation in rice. • SA alleviates Cd toxicity. • The filling stage is the key period for SA to reduce Cd in rice grain. [ABSTRACT FROM AUTHOR]

Abstract The objective of this paper is to study the number and stability of limit cycles for planar piecewise linear (PWL) systems of node–saddle type with two linear regions. Firstly, we give a thorough analysis of limit cycles for Liénard PWL systems of this type, proving one is the maximum number of limit cycles and obtaining necessary and sufficient conditions for the existence and stability of a unique limit cycle. These conditions can be easily verified directly according to the parameters in the systems, and play an important role in giving birth to two limit cycles for general PWL systems. In this step, the tool of a Bendixon-like theorem is successfully employed to derive the existence of a limit cycle. Secondly, making use of the results gained in the first step, we obtain parameter regions where the general PWL systems have at least one, at least two and no limit cycles respectively. In addition for the general PWL systems, some sufficient conditions are presented for the existence and stability of a unique one and exactly two limit cycles respectively. Finally, some numerical examples are given to illustrate the results and especially to show the existence and stability of two nested limit cycles. Highlights • The piecewise linear (PWL) system is of node–saddle type. • A necessary and sufficient condition is presented for the uniqueness of a limit cycle for Liénard PWL systems. • The number of limit cycles are given in different parameter regions for general PWL systems. • A Poincaré–Bendixon-like theorem for Filippov systems is successfully employed to obtain the existence of a limit cycle. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept named the weak flocking behavior. That is, if the complex system has the weak flocking property, the agents do not need have the same velocities to keep together when t → ∞. This shows the biggest difference between weak flocking behavior and the flocking behavior. The advantage of this concept is that its practical significance—the agents don't need always keep in step in lots of the complex systems but they still keep together. Then, we propose a weak flocking model with two agents and study two different mechanisms for this model. Moreover, we also consider a system with N agents. Under the weak link mechanism, the system with N agents can keep weak flocking. [ABSTRACT FROM AUTHOR]