Many experiments have evidenced the transition with different time scales from short-term memory (STM) to long-term memory (LTM) in mammalian brains, while its theoretical understanding is still under debate. To understand its underlying mechanism, it has recently been shown that it is possible to have a long-period rhythmic synchronous firing in a scale-free network, provided the existence of both the high-degree hubs and the loops formed by low-degree nodes. We here present a simplified memory network model to show that the self-sustained synchronous firing can be observed even without these two necessary conditions. This simplified network consists of two loops of coupled excitable neurons with different synaptic conductance and with one node being the sensory neuron to receive an external stimulus signal. This model can be further used to show how the diversity of firing patterns can be selectively formed by varying the signal frequency, duration of the stimulus and network topology, which corresponds to the patterns of STM and LTM with different time scales. A theoretical analysis is presented to explain the underlying mechanism of firing patterns. U nderstanding the brain is the most challenging problem in biology, neuroscience and network science. To figure out the underlying mechanisms, numerous experiments have been designed and several brain imaging techniques have been developed such as the computed tomography (CT), electroencephalography (EEG), positron emission tomography (PET), and functional magnetic resonance imaging (fMRI) etc 1,2 . By using these techniques, we now understand much better the events related to cognitive tasks and brain diseases such as seizure etc. Among all these events, memory is probably the one gotten the most attention so far. It has been revealed that the process of memory has three sequence stages, from sensory memory(SM) to shortterm memory (STM) and then to long-term memory (LTM) 3-8 . SM is brief, transient sensations, typically between 200 ms and 500 ms after the brain's cerebral cortex receives nerve information from ears, eyes and touch sensors. STM extracts messages from SM and can be maintained by active rehearsal and are easily displaced by new information or distractions. STM maintains information for a brief period before it is manipulated and is usually referred to as working memory 9-11 . The maintenance and manipulation of working memory is described as the executive control of working memory. STM may persist for minutes. LTM comes from STM and is maintained by more stable and permanent changes in neural connections widely spread throughout brain. LTM can last for hours, days, or even years. Many areas of cortex are involved in STM (prefrontal, parietal, frontal eye fields), but hippocampus in brain is the key region for LTM, which receives information from cortex via multiple parallel pathways to each of its main subregions and is essential to transfer neural information from STM to LTM. When the hippocampus is damaged, the brain can not transfer new memories into LTM 12 . Under different behavior conditions, hippocampal networks show rhythmic oscillations in various frequency ranges such as theta (5-10 Hz) and gamma (30-100 Hz) frequency rhythms observed in the rat during exploration and rapid eye movement sleep 13, 14 . It has been pointed out that different LTM correspond to different pattern dynamics in the brain network 13, [15] [16] [17] , and interactions between neurons through synaptic links provide powerful computation capacities of the brain 18, 19 . Further, it was revealed that the recurrent excitatory loops within a neural networks such as the cortico-striato-thalamo-cortical loop can sustain a persistent activity or pattern without external stimulus 20,21 . To understand the mechanism of the above experimental findings, the coupled oscillator theory has been widely used to investigate the interaction among neurons. For example, it was pointed out that there is a largescale cortical synchronization 22,23 and synfire propagation in cognitive process where the signal is carried by a wave of synchronous neuronal activity within a subset of network neurons 14, [24] [25] [26] . The corresponding theoretical studies have confirmed the solution of traveling waves in 1D and 2D medium [27] [28] [29] [30] [31] . Moreover, theoretical studies show that it is even possible to observe a localized states, called bump attractor in 1D lattice of coupled neurons, which is related to the working memory 32,33 . However, most cognitive functions are not represented in the brain OPEN SUBJECT AREAS: NONLINEAR PHENOMENA COMPLEX NETWORKS
Xu REF presented a simplified memory network aimed at pattern formation; they used two loops of coupled neuron to analyze the process from short-term to long-term memory theoretically.
A simplified memory network model based on pattern formations
Scientific Reports
Scientific Reports
Computer Science Medicine