Modularity Q has been broadly used as a valid measure for community detection in complex networks. Fortunato and Barthélemy later proposed that modularity contains an intrinsic scale that depends on the total number of links in the network. But some extra restrictions on some parameters are needed for their analysis. In this paper we further study this problem. Here we give general analysis and...

We study the problem of stabilizing exponentially unstable linear systems with saturating actuators. The study begins with planar systems with both poles exponentially unstable. For such a system, we show that the boundary of the domain of attraction under a saturated stabilizing linear state feedback is the unique stable limit cycle of its time-reversed system. A saturated linear state feedbac...

We consider the class of polynomial differential equation x = 2 ( , ) ( , ) ( , ) n n m n m P x y P x y P x y + + + + , 2 ( , ) ( , ) ( , ) n n m n m y Q x y Q x y Q x y + + = + + . For , 1 m n ≥ where i P and i Q are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditi...

The global stability of a multi-species interacting system has apparently important biological implications. In this paper we study the global stability of Gause-type predator-prey models by providing new criteria for the nonexistence of cycles and limit cycles. Our criteria have clear geometrical interpretations and are easier to apply than other methods employed in recent studies. Using these...

Transitions between low (L-mode) and intermediate (I-phase) confinement regimes triggered by sawteeth are investigated by using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak. The I-phase is characterized by limit cycle oscillations (LCOs). Repeated L-I-L transitions induced by sawtooth heat pulses are also observed. The statistical analyses show that the delay time of ...