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We analyse the possible dynamical states emerging for two symmetrically pulse coupled populations of leaky integrate-and-fire neurons. In particular, we observe broken symmetry states in this set-up: namely, breathing chimeras, where one population is fully synchronized and the other is in a state of partial synchronization (PS) as well as generalized chimera states, where both populations are in PS, but with different levels of synchronization. Symmetric macroscopic states are also present, ranging from quasi-periodic motions, to collective chaos, from splay states to population anti-phase partial synchronization. We then investigate the influence disorder, random link removal or noise, on the dynamics of collective solutions in this model. As a result, we observe that broken symmetry chimera-like states, with both populations partially synchronized, persist up to 80 % of broken links and up to noise amplitudes 8 % of threshold-reset distance. Furthermore, the introduction of disorder on symmetric chaotic state has a constructive effect, namely to induce the emergence of chimera-like states at intermediate dilution or noise level.
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a networks level of dilution and asymmetry. The network dilution measur
The thermodynamic and retrieval properties of the Blume-Emery-Griffiths neural network with synchronous updating and variable dilution are studied using replica mean-field theory. Several forms of dilution are allowed by pruning the different types o
The effects of a variable amount of random dilution of the synaptic couplings in Q-Ising multi-state neural networks with Hebbian learning are examined. A fraction of the couplings is explicitly allowed to be anti-Hebbian. Random dilution represents
The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on a recurren
The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of both layered feedforward and fully connected neural network models with synaptic noise. These two types of architectures require a different method to be solve