Formation Control of Swarming Vessels Using a Virtual Matrix Approach and ISOT Guidance Algorithm

The formation control for the effective operation of multiple vessels is discussed. First, a virtual matrix approach is proposed to improve the formation robustness and transform performance during swarm operations, which is created based on the virtual leader vessel location, and agents composing the formation follow cells in the matrix to maintain formation. This approach is affected by the virtual leader vessel location. The virtual leader vessel location is defined by two cases: matrix center and geometric center; furthermore, robustness and efficiency comparison simulations are performed. The simulation results show that in most formations, the geometric center is better in terms of efficiency and robustness. Second, the isosceles triangle guidance algorithm is proposed to improve the “go-back behavior” of certain agents during excessive maneuvering. Through a waypoint-following simulation, the algorithm is confirmed to be superior to the line-of-sight guidance algorithm. The swarm simulation on the virtual map verifies the performance of the proposed formation n control and guidance algorithm.

Bifurcations, Complex Behaviors, and Dynamic Transition in a Coupled Network of Discrete Predator-Prey System

The nonlinear dynamics of predator-prey systems coupled into network is an important issue in recent biological advances. In this research, we consider each node of the coupled network represents a discrete predator-prey system, and the network dynamics is investigated. By applying Jacobian matrix, center manifold theorem and bifurcation theorems, stability of fixed points, flip bifurcation and Neimark-Sacker bifurcation of the discrete predator-prey system are analyzed. Via the method of Lyapunov exponents, the nonchaos-chaos transition of the coupled network along the routes to chaos induced by bifurcations is determined. Numerical simulations are performed to demonstrate the bifurcations, various attractors and dynamic transitions of the coupled network. Via comparison, we find that the coupled network exhibits far richer and more complex behaviors than single predator-prey system, including period-doubling cascades in orbits of period-2, period-4, period-8, invariant closed curves, dynamic windows for periodic orbits and invariant curves, quasiperiodic orbits, tori, and chaotic sets. Moreover, the attractors of the coupled network show more diverse and complicated structures. These results may provide a new perspective on the predator-prey dynamics in complex networks.