A comprehensive review of spatiotemporal pattern formation in systems driven away from
equilibrium is presented, with emphasis on comparisons between theory and quantitative …

Synchronization phenomena in large populations of interacting elements are the subject of
intense research efforts in physical, biological, chemical, and social systems. A successful …

What happens in our brain when we make a decision? What triggers a neuron to send out a
signal? What is the neural code? This textbook for advanced undergraduate and beginning …

The synchronization of coupled oscillators is a fascinating manifestation of self-organization
that nature uses to orchestrate essential processes of life, such as the beating of the heart …

Populations of coupled oscillators may exhibit two coexisting subpopulations, one with
synchronized oscillations and the other with unsynchronized oscillations, even though all of …

Neurons in the brain communicate by short electrical pulses, the so-called action potentials
or spikes. How can we understand the process of spike generation? How can we …

Assemblages of microscopic colloidal particles exhibit fascinating collective motion when
energized by electric or magnetic fields. The behaviors range from coherent vortical motion …

Several neural network models in continuous time are reconsidered in the framework of a
general mean-field theory which is exact in the limit of a large and fully connected network …

We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions.
New phenomena include bistability between synchronized and incoherent states, and …

We show that series arrays of N identical overdamped Josephson junctions have extremely
degenerate dynamics. In particular, we prove that such arrays have N− 3 constants of motion …