Traveling Wave Solution of the Olver–Rosenau Equation Solved by Dynamics System

Olver–Rosenau equations presented by Olver and Rosenau can be rewritten to the dynamic system by the wave transformation. The system is a Hamiltonian system with the first integral, and its phase-space and equilibrium point analysis are given in different parameter spaces in detail. On this basis, we can derive various solutions of the original equation relating these orbits in different phase-space planes, and the theoretical basis of the numerical solution is provided for engineering application and production practice.

Oscillation phenomenon and its mechanism of an energy-saving and emission-reduction system

Purpose This paper aims to study the oscillation phenomenon before chaos as well as its mechanism of occurrence in the energy-saving and emission-reduction system. Design/methodology/approach The system dynamics analysis, phase portrait analyses, equilibrium point analysis and bifurcation curve were applied to this paper. Findings First, the authors find an oscillation phenomenon previous to chaos. Second, on the one hand, the existence of two unstable saddles is the reason for the occurrence of oscillation phenomenon. On the other hand, the increasing of carbon emissions can arouse oscillation phenomenon. Originality/value This paper finds an oscillation phenomenon previous to chaos in the energy-saving and emission-reduction system. The mechanism of occurrence of oscillation phenomenon is studied. The existence of two unstable saddles is the reason for the occurrence of such oscillation phenomenon. The oscillation is related with fold bifurcation. The study also provides a theoretical basis for the further study of chaos control.

Consensus Equilibrium Point Analysis for Heterogeneous Multi-Agent System in Undirected Graph

The consensus problem of heterogeneous multi-agent systems is investigated. A linear consensus protocol is proposed for this system. Aiming at consensus condition can be only obtained, but the consensus equilibrium point cannot be obtained in this study, the consensus equilibrium point is derived by applying graph theory and matrix theory in this paper. Finally, a numerical simulation is provided to illustrate the effectiveness of the theoretical result.