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This paper is concerned with the dynamics of autonomous agents in performing distributed problem-solving tasks. The goal of this work is to show: 1) how certain tasks may be handled by breeds of distributed agents self-reproduced by other agents in response to their local environment and 2) how the behavioral repository of the agents may be constructed based on some well-defined dynamical systems models. The breeds of agents progressively generated in the course of distributed problem-solving are referred to as agentlets. The specific task for demonstrating this dynamical systems-based agentlet-oriented approach is the one in which the agents are required to search and mark certain feature locations in a two-dimensional (2-D) search space by way of divide-and-conquer. In so doing, individual agents may have different dynamical motion, depending on when and where they are bred. This paper provides a detailed description of the agents of different dynamics and shows how the agentlets proceed with this task by moving according to their well-defined dynamics, breeding their offspring agents in the environment., and fine-tuning their dynamical systems parameters. In addition, it is proven that in the given example task, the designed agentlets will guarantee to reach all the feature locations in the search space.