A nonlinear convective system with oscillatory behaviour for certain parameter regimes

Abstract

The behaviour of a fluid system governed by a quadratic equation of state for the temperature is studied. The model consists of two well-mixed and interconnected vessels subjected to external thermal forcing. If inertial effects are neglected the temperature response of the fluid is governed by two autonomous ordinary differential equations in time. An investigation of these equations revealed that, depending upon the choice of parameters, the system has two possible final states: one stationary, the other a relaxation oscillation. The transitions between these states occur as sub- and supercritically unstable Hopf bifurcations. For certain parameter ranges, a stationary solution can thus coexist with a relaxation oscillation, the initial conditions determining which of these is realized.