are stable everywhere except at the vicinity of $\Delta \e \sim N^{-2/3}$ of their end-points $\e_{coll}$ and $\e_{expl}$ [@ka2; @chi], where $N$ is the number of particles in the system. Hence it is natural to assume that once the energy of the system in the uniform state is set sufficiently near above or below $\e_{coll}$, the system will undergo a collapse to a core-halo state with the same energy and higher entropy. Similarly, if the energy of the core-halo system is set sufficiently near below or above $\e_{expl}$, the system will undergo an explosion bringing it to a uniform state with the same energy and higher entropy. Our goal here is to study if and how such collapse and explosion proceed in a realistic three-dimensional N-particle dynamical system.

The paper is organized as follows. In the next section we formally introduce the system, outline the MF analysis and describe the MD setup. Then, we present the simulation results for the equilibrium uniform and core-halo states and compare them to the MF predictions. After that we describe and interpret the observed dynamics of the collapse and the explosion transitions. A discussion of the obtained results concludes the paper.

simulation
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We 