In excitable systems, such as neuronal networks, many important properties depend on inhibition mechanisms. Inhibition stabilizes network dynamics, controls activity rhythms and regulates pattern formation. For the brain and sensory systems, inhibition seems to be essential in information encoding and learning. From the perspective of Self-organized criticality, inhibition is commonly viewed as one of the system control parameters, it means a parameter which can promote transition from an active to an absorbing state if its strength surpasses a critical value. However, the models typically consider fully connected networks, where the excitatory and inhibitory interactions have a global effect. In this work, we show that, when the supposition of a complete graph is not satisfied, inhibition strength is not a control parameter in the sense that it cannot promote transitions from active to absorbing states and vice versa. Although inhibitory strength does not seem to play a role in the phase transition, the proportion of inhibitory neurons in the network does it. We present approximated analytical and simulation results in a network of stochastic leaky, integrate-and-fire neurons (SLIF). We give simple, intuitive explanations of how the differences between excitatory and inhibitory effects over network dynamics handle an asymmetric role over the phase transition.

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