Brain plasticity or neuroplasticity refers to the ability of the nervous system to reorganise itself in response to stimuli. For instance, sensory and motor stimulation, memory formation, and learning depend on brain plasticity. Neuronal synchronisation can be enhanced or suppressed by the plasticity. Synchronisation is related to many functions in the brain, as well as to some brain disorders. One possible plasticity rule is the burst-timing-dependent plasticity (BTDP), that induces synaptic alteration according to the timing of neuronal bursts. In this work, we build a network of coupled Rulkov maps where the excitatory connections are randomly distributed. We consider the BTDP to study its effects on the synchronous neuronal activities. In our simulations, we observe that depending on the initial synaptic weights, the whole network or part of it can have its neuronal synchronisation improved. This increase can be reached by two different mechanisms, the initial burst synchronisation and random statistical coincidence. A mix of these two mechanism is also found in the network. BTDP can induce the formation of desynchronised and synchronised clusters that operate in different frequencies, but only if the noise level is low. Our results show possible mechanisms of cluster formation in burst neuronal networks. We also consider the BTDP rule on a small-world network and show that, depending on the initial connection strength, the network can exhibit local or non-local properties.

脑可塑性或神经可塑性是指神经系统响应刺激而自我重组的能力。例如，感觉和运动刺激，记忆形成和学习取决于大脑可塑性。可塑性可增强或抑制神经元同步。同步与大脑中的许多功能以及某些脑部疾病有关。一种可能的可塑性规则是依赖于爆发时间的可塑性（BTDP），它会根据神经元爆发的时间诱导突触改变。在这项工作中，我们建立了耦合的Rulkov映射网络，其中的激励连接是随机分布的。我们认为BTDP可以研究其对同步神经元活动的影响。在我们的模拟中，我们观察到，根据初始突触权重，整个网络或部分网络可以改善其神经元同步性。这种增加可以通过两种不同的机制来实现，即初始突发同步和随机统计符合。在网络中也可以找到这两种机制的混合体。BTDP可以诱导以不同频率运行的非同步和同步集群的形成，但前提是噪声水平较低。我们的结果显示了爆发神经元网络中簇形成的可能机制。我们还考虑了小世界网络上的BTDP规则，并表明，根据初始连接强度，网络可以显示本地或非本地属性。在网络中也可以找到这两种机制的混合体。BTDP可以诱导以不同频率运行的非同步和同步集群的形成，但前提是噪声水平较低。我们的结果显示了爆发神经元网络中簇形成的可能机制。我们还考虑了小世界网络上的BTDP规则，并表明，根据初始连接强度，网络可以显示本地或非本地属性。在网络中也可以找到这两种机制的混合体。BTDP可以诱导以不同频率运行的非同步和同步集群的形成，但前提是噪声水平较低。我们的结果显示了爆发神经元网络中簇形成的可能机制。我们还考虑了小世界网络上的BTDP规则，并表明，根据初始连接强度，网络可以显示本地或非本地属性。