Stability and Competition in Multi-spike Models of Spike-Timing Dependent Plasticity
Fig 5
Stability and competition in the suppression model.
A. Fixed points of ⟨w⟩ as functions of the ratio between the potentiation and depression time constants. The stable fixed point disappears beyond the critical value τ+/τ− < 1.2. When the ratio approaches the critical value, the fixed point grows rapidly (gray area), leading to a stable distribution. B. The average drift when τ+/τ− = 1. The solid curve shows the analytical result (Eq 6) and the boundaries of gray shading is obtained by simulations. The filled circle is the stable fixed point. C. The average drift when τ+/τ− = 1.1. The stable fixed point moves to larger values than in B. D. The average drift when τ+/τ− = 1.5. No nontrivial fixed point exists. E. The partially stable bimodal steady-state distribution of weights corresponding to the parameters of B. F. The stable steady-state distribution of weights corresponding to the parameters of C. G. The unstable steady-state distribution of weights clustered around the upper bound corresponding to the parameters of D, when no stable fixed point exists. H-J. Competition between correlated and uncorrelated synapses with parameter corresponding to E-G. The competition is anti-Hebbian in all cases.