Burst firing creates an attractor in synaptic weight dynamics.

Neural circuits often alternate between tonic and burst firing, two distinct activity regimes that reflect changes in excitability and neuromodulatory state. While tonic firing produces asynchronous spikes driven by diverse external inputs, collective burst firing consists of rapid clusters of spikes followed by a period of silence, happening synchronously within the network. Synaptic plasticity has typically been studied only in either one of these regimes, leaving unclear how their distinct plasticity dynamics can be combined when circuits alternate between regimes. Here, we use a conductance-based network model endowed with calcium-based or spike-timing-based plasticity rules to examine how synaptic weights evolve across tonic and burst firing regimes. During tonic firing, synaptic weights are driven by the statistics of external inputs, producing a broad distribution across the network. In contrast, during collective burst firing, weights converge to a narrow region in weight space: a burst-induced attractor. We derive the location of this attractor analytically in terms of plasticity parameters and activity statistics, and confirm its emergence across diverse plasticity rules. The attractor reflects the synchronization of plasticity-driving signals during bursts, which homogenizes synaptic dynamics and forces convergence toward shared fixed points. We further show that neuromodulation and synaptic tagging can shift or split the burst-induced attractor, stabilizing selected synapses while weakening others. Together, these results identify burst-induced attractors as a robust emergent property of collective bursting. Alternation between tonic and burst firing provides a biologically plausible context in which heterogeneous, input-driven synaptic configurations formed during tonic activity can be selectively consolidated or down-selected by the burst-induced attractor during subsequent bursts. By showing how they can be analytically predicted and experimentally modulated, our work provides a general computational framework linking firing state transitions, synaptic plasticity, and memory organization.