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This thesis focuses on the demonstration of the existence of and anal ysis of phenomena related to the discontinuous non-equilibrium phase transition betwe en an active (or reactive) state and a poisoned (or extinguished) state occur ring in a stochastic lattice-gas realization of Schloegl’s second model for autocatalysis . This realization, also known as the Quadratic Contact Process , involves spontaneous annihilation, autocatalytic creation, and diffusion or hopping of particles on a square lattice, where creation a t empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates p>0 and is an absorbing particle-free “vacuum” state. The populated active steady state exists just for p below a critical value, p e. Our initial studies without particle hopping demonstrated a dependence on orientation or slope, S, of the equistability or stationary point p=peq(S) for a planar interface separating active and poisoned states. They also s howed that p e = peq(S=1) for diagonal interfaces. This orientation dependence was shown to e xtend to non-zero hop rates h>0, but to quickly weaken with increasing h. If p f denotes the critical value below which a finite population can survive, then we show that p f =peq(S=0) and that p f < pe. This strict inequality contrasts a postulate of Durrett, and is a direct conseque nce of the occurrence of coexisting stable active and poisoned states for a finite ra nge pf ≤ p ≤ pe. Although this socalled generic two-phase coexistence (2PC) contrasts behavior in the rmodynamic systems. However, one still finds metastability and nucleation phenomena simil ar to those in discontinuous equilibrium transitions. We also provide a theoretical fr amework for analysis of such metastability phenomena. Extensions of the basic model are c onsidered to different lattices and to introduce tricritical behavior. Most precise ana lysis was performed with

Generic two-phase coexistence in the quadratic contact process