Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses. We find that both coupling modes play a crucial role by the synchronization of the network. In addition, delayed inhibitory synapses affect the emerging oscillatory patterns. By increasing the inhibitory synaptic delay, we observe a transition from regular to mixed oscillatory patterns at a critical value. We also examine how the unreliability of inhibitory synapses influences the emergence of synchronization and the oscillatory patterns. We find that low levels of reliability tend to destroy synchronization and, moreover, that interneuronal networks with long inhibitory synaptic delays require a minimal level of reliability for the mixed oscillatory pattern to be maintained.

The optimal consensus problem of asynchronous sampling single-integrator and double-integrator multiagent systems is solved by distributed model predictive control (MPC) algorithms proposed in this article. In each predictive horizon, the finite-time linear-quadratic performance is minimized distributively by the control input with consensus state optimization. The MPC technique is then utilized to extend the optimal control sequence to the case of an infinite horizon. Conditions depending only on each agent's weighting scalar and sampling step are derived to guarantee the stability of the closed-loop system. Numerical examples of rendezvous control of multirobot systems illustrate the efficiency of the proposed algorithm.

We study the dependence of synchronization transitions in scale-free networks of bursting neurons with hybrid synapses on the information transmission delay and the probability of inhibitory synapses. It is shown that, irrespective of the probability of inhibitory synapses, the delay always plays a subtle role during synchronization transition of the scale-free neuronal networks. In particular, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. In addition, it is found that, for smaller and larger probability of inhibitory synapses, intermittent synchronization transition is relatively profound, while for the moderate probability of inhibitory synapses, synchronization transition seems less profound. More interestingly, it is found that as the probability of inhibitory synapses is large, regions of synchronization are upscattering.