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In this paper, we explore the mechanisms of central pattern generators (CPGs), circuits that can generate rhythmic patterns of motor activity without external input. We study the half-center oscillator, a simple form of CPG circuit consisting of neurons connected by reciprocally inhibitory synapses. We examine the role of asymmetric coupling factors in shaping rhythm activity and how different network topologies contribute to network efficiency. We have discovered that neurons with lower synaptic strength are more susceptible to noise that affects rhythm changes. Our research highlights the importance of asymmetric coupling factors, noise, and other synaptic parameters in shaping the broad regimes of CPG rhythm. Finally, we compare three topology types' regular regimes and provide insights on how to locate the rhythm activity. [ABSTRACT FROM AUTHOR]