| The phenomenon of aggregation growth is popular and important for a wide variety of fields in nature, such as physics, biology, chemistry, medicine and sociology. The originally studied mechanism is the pure cluster-cluster aggregation process, but recently the researches had been steadily extended to aggregation phenomena with much complex mechanisms. Especially, much attention has been devoted to the generalized aggregation phenomena in sociology and economy.In this paper, using mean-field theory and Smoluchowski rate equation, we studied the influence of catalyzed-birth and catalyzed-death to the scaling behaviors of the conventional migration-driven aggregation process in sociology and economy. The content of this paper includes:Two catalyzed-birth models of n-species aggregates with migration-driven growth processes are proposed and studied. In the first catalyzed-birth model, the evolution behavior of aggregate-size distribution a_k~1(t) of A~1 species depends crucially on the value of the catalysis rate parameterν: (1) a_k~1(t)obeys the conventional scaling law in the case ofν<0, (2) a_k~1(t) satisfies a modified scaling form in the case ofν>0. In the second mutually catalyzed-birth model, the kinetic behaviors of the system are found to fall into two categories for the differentν: (1) growth obeying conventional scaling form withy≤0, (2) gelling at finite time withν> 0.A migration-driven aggregation model and a self-aggregation growth model of three-species with the competition between catalyzed-birth and catalyzed-death are proposed and studied. The results tells: (1) when the migration-driven aggregation (self-aggregation) dominates the process, a_k(t) satisfies the conventional scaling form, (2) when the catalyzed-birth dominates the process, a_k(t) satisfies the conventional or modified scaling form, (3) when the catalyzed-death dominates the process, the scaling description of the aggregate-size distribution of the system breaks down completely.
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