Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information processing. Dynamic mean-field theory yields the statistics of the activity, the maximum Lyapunov exponent, and the memory capacity of the network. We find an exact condition that determines the transition from stable to chaotic dynamics and the sequential memory capacity in closed form. The input suppresses chaos by a dynamic mechanism, shifting the transition to significantly larger coupling strengths than predicted by local stability analysis. Beyond linear stability, a regime of coexistent locally expansive, but non-chaotic dynamics emerges that optimizes the capacity of the network to store sequential input.

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Change is ubiquitous in living beings. In particular, the connectome and neural representations can change. Nevertheless, behaviors and memories often persist over long times. In a standard model, associative memories are represented by assemblies of strongly interconnected neurons. For faithful storage these assemblies are assumed to consist of the same neurons over time. Here we propose a contrasting memory model with complete temporal remodeling of assemblies, based on experimentally observed changes of synapses and neural representations. The assemblies drift freely as noisy autonomous network activity and spontaneous synaptic turnover induce neuron exchange. The gradual exchange allows activity-dependent and homeostatic plasticity to conserve the representational structure and keep inputs, outputs, and assemblies consistent. This leads to persistent memory. Our findings explain recent experimental results on temporal evolution of fear memory representations and suggest that memory systems need to be understood in their completeness as individual parts may constantly change.

Jellyfish nerve nets provide insight into the origins of nervous systems, as both their taxonomic position and their evolutionary age imply that jellyfish resemble some of the earliest neuron-bearing, actively-swimming animals. Here, we develop the first neuronal network model for the nerve nets of jellyfish. Specifically, we focus on the moon jelly Aurelia aurita and the control of its energy-efficient swimming motion. The proposed single neuron model disentangles the contributions of different currents to a spike. The network model identifies factors ensuring non-pathological activity and suggests an optimization for the transmission of signals. After modeling the jellyfish’s muscle system and its bell in a hydrodynamic environment, we explore the swimming elicited by neural activity. We find that different delays between nerve net activations lead to well-controlled, differently directed movements. Our model bridges the scales from single neurons to behavior, allowing for a comprehensive understanding of jellyfish neural control of locomotion.

Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state. We propose a simple spiking model for developing neural networks, showing how these may "grow into" criticality. Avalanches generated by our model correspond to clusters of widely applied Hawkes processes. We analytically derive the cluster size and duration distributions and find that they agree with those of experimentally observed neuronal avalanches.

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8Jellyfish nerve nets provide insight into the origins of nervous systems, as both their taxonomic 9 position and their evolutionary age imply that jellyfish resemble some of the earliest 10 neuron-bearing, actively-swimming animals. Here we develop the first neuronal network model for 11 the nerve nets of jellyfish. Specifically, we focus on the moon jelly Aurelia aurita and the control of 12 its energy-efficient swimming motion. The proposed single neuron model disentangles the 13 contributions of different currents to a spike. The network model identifies factors ensuring 14 non-pathological activity and suggests an optimization for the transmission of signals. After 15 modeling the jellyfish's muscle system and its bell in a hydrodynamic environment, we explore the 16 swimming elicited by neural activity. We find that different delays between nerve net activations 17 lead to well-controlled, differently directed movements. Our model bridges the scales from single 18 neurons to behavior, allowing for a comprehensive understanding of jellyfish neural control. Nervous Systems of Scyphomedusae 44The nervous system of scyphozoan jellyfish consists of several neuronal networks, which are 45 distributed over the entire jellyfish bell, the tentacles and the endoderm (Schäfer, 1878; Passano 46 and Passano, 1971). The only obvious points of concentration of a larger number of neurons are the 47

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