Modeling of Self-sustained Neuron Population without External Stimulus

Understanding the neurobiological mechanisms underlying self-referential cognition and baseline self-consciousness remains a fundamental challenge in computational neuroscience. In this work, we propose a large-scale computational model incorporating a 10,000-neuron spiking neural network (SNN) based on Izhikevich dynamics. The network is structured into two interacting subsystems: a sensory processing layer (5,000 regular-spiking cortical neurons) and an endogenous Default Mode Network (DMN) pacemaker subsystem (5,000 intrinsically bursting neurons). The DMN layer is modulated by continuous tonic currents reflecting ascending brainstem neuromodulation, maintaining intrinsic, autonomous bioelectric rhythms independent of external sensory input. To represent top-down cognitive modulation, synaptic weights are hierarchically structured such that DMN-to-network projections exceed sensory-level connections. Through numerical simulations using a modified two-step Euler integration scheme, we demonstrate how endogenous pacemaker activity interacts with transient external sensory perturbations, providing an elementary mathematical framework for the emergence of a persistent, self-sustaining neural representation of "Self".

We construct a minimal but biologically plausible spiking neuron model operating in discrete time, combining multiplicative spike-timing-dependent plasticity (WSTDP), divisive normalization of synaptic integration, homeostatic threshold adaptation, and a one-step refractory period. We show that this normalization admits a biologically plausible dendritic implementation in which each binary junction operates using only locally available information. Assembling excitatory-inhibitory pairs of such neurons into a two-dimensional recurrent network and applying periodic localized stimulation, we find that the network spontaneously gives rise to stable, self-propagating wave packets with the properties of dissipative solitons: they maintain a stable spatial profile, propagate at constant speed, and annihilate upon frontal collision. Their emergence requires a geometric asymmetry between excitatory and inhibitory connection radii, and initial inhibitory synapses stronger than excitatory ones. WSTDP engraves the direction of propagation into the synaptic weight profile, so that the network learns by itself to sustain propagation in one direction while suppressing the reverse. When two sources are active simultaneously, the resulting waves annihilate upon collision, defining a semi-persistent boundary whose position encodes the relative phase and frequency of the two sources. These results provide a minimal computational framework for studying the emergence of cortical traveling waves, activity zone delimitation, and spatial memory from local plasticity rules alone.

Balanced spiking networks can transition between silent, asynchronous-irregular, and oscillatory states depending on interacting synaptic and temporal time scales, while their joint parameter structure remains incompletely characterized. In this work, we systematically map how postsynaptic decay (τs), conduction delay (d), and plasticity rate (λp) jointly shape oscillatory regimes in recurrent leaky integrate-and-fire networks. By combining Brian2 simulations across the (τs, d, λp) space with a coarse Hopf-reference boundary, we construct regime maps that directly visualize SIL-AI-OSC transitions and corresponding spectral prominence landscapes. The mapped results show that increasing λp expands oscillatory regions toward shorter τs and moderate-to-long delays, while prominence maps identify parameter regions with the strongest rhythmic coherence. Representative control experiments further connect this global landscape to local rhythm-forming mechanisms, showing that STDP freezing weakens rhythmic coherence whereas delay jitter enhances it with minimal change in mean firing rate. As a result, these findings provide a useful reference for operating-point selection, synchrony modulation studies, and future biologically grounded spiking-network modeling within similar balanced-network settings.