Bifurcation and chaos analysis for a discrete ecological developmental systems.

This work concentrates on the dynamic analysis including bifurcation and chaos of a discrete ecological developmental systems. Specifically, it is a prey-predator-scavenger (PPS) system, which is derived by Euler discretization method. By choosing the step size h as a bifurcation parameter, we determine the set consists of all system's parameters, in which the system can undergo flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB). The theoretical results are verified by some numerical simulations. It is shown that the discrete systems exhibit more interesting behaviors, including the chaotic sets, quasi-periodic orbits, and the cascade of period-doubling bifurcation in orbits of periods 2, 4, 8, 16. Finally, corresponding to the two bifurcation behaviors discussed, the maximum Lyapunov exponent is numerically calculated, which further verifies the rich dynamic characteristics of the discrete system.

Multi-formation control of nonlinear leader-following multi-agent systems.

This paper deals with the multi-formation control problem for nonlinear leader-following multi-agent systems. Both the fixed topology case and the switching topology case are considered. The neighbor-based multi-formation control protocols are proposed under the assumption that for one subgroup, the total information received from other subgroups is zero. Then, based on the Lyapunov stability theory combined with the algebraic graph theory, sufficient conditions are established to ensure that the leader-following multi-agent systems with nonlinear dynamics can reach and maintain the desired multi-formation control. Finally, simulation examples are provided to illustrate the effectiveness of the theoretical results.

Performance limitations of networked control systems with quantization and packet dropouts.

This paper investigates the problem of optimal tracking performance of networked control systems (NCSs) with quantization and packet-dropouts. The system under consideration is linear time-invariant (LTI), multi-input multi-output (MIMO), where an H2 norm of error signal between the reference input and the system output is used as the tracking performance index. The impacts of packet-dropouts in the communication channel and the quantized input and output are studied. The goal is to obtain the minimal error in tracking a random signal, by searching through all possible stabilizing two-parameter controllers. It is shown that, the minimum value of tracking error is closely related to the reference input signal direction, the non-minimum phase zeros and unstable poles of the given plant, including the locations and directions. We also demonstrated the quantization error and the packet-dropouts may degrade the tracking performance. A typical example is given to evaluate the theoretical results.

Stability and bifurcation analysis of new coupled repressilators in genetic regulatory networks with delays.

The genetic regulatory networks are complex dynamic systems which reflect various kinetic behaviors of living things. In this paper, a new structure of coupled repressilators is introduced to exploit the underlying functions. The new coupled repressilator model consists of two identical repressilators inhibiting each other directly. The coupling delays are taken into account. The existence of a unique equilibrium for this system is verified firstly, then the stability criteria for equilibrium are analyzed without and with coupling delays. The different functions on equilibrium and its stability played by related biochemical parameters in the structure including maximal transcription rate, coupling strength, the decay rate ratio between proteins and mRNAs, and coupling delays are discussed. At last, several numerical simulations are made to demonstrate our results.

Performance limitations in the tracking and regulation problem for discrete-time systems.

In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.