Abstract: For simplified analytic model of rockburst in narrow coal pillar, the catastrophe model of rockburst in narrow coal pillar belongs to the fold catastrophe model and can be educed by equilibrium relation of work-energy increment from energy conservation principle. All characteristics, demonstrated by the equilibrium equation and its equilibrium path of the catastrophe model, can describe all behaviors including system's stability of failure process in coal pillar by form of rockburst and gradual damage one by one correspondingly. The curve of elastic energy changing rate of rock beam, which includes abundant information, is given for the first time; it has great significance in understanding the behavior and law of rock beam- coal pillar's system in each phase. Parlance and expression, given in the article, that energy importing rate J = 0 is system destabilization critical condition implicates Cook stiffness criterion, so it's a dynamic generalization of Cook criterion in the form of energy. Using energy importing rate, understanding in the stability of rock-coal system under ultimate state can be improved from qualitative understanding to quantitative description; and the expression of the stability of rock-coal system is also endue with a new form.

Key words: rockburst in pillar, work- energy increment&rsquo, equilibrium relation, fold catastrophe model, energy importing rate, energy releasing rate