Convergent activation dynamics in continuous time networks
Neural Networks
Analysis of neural excitability and oscillations
Methods in neuronal modeling
Evolving dynamical neural networks for adaptive behavior
Adaptive Behavior
On the dynamics of small continuous-time recurrent neural networks
Adaptive Behavior - Special issue on computational neuroethology
SIAM Journal on Numerical Analysis
Weakly connected neural networks
Weakly connected neural networks
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Phase-plane analysis of neural activity
The handbook of brain theory and neural networks
The Mathematica Book
Attractor Landscapes and Active Tracking: The Neurodynamics of Embodied Action
Adaptive Behavior - Animals, Animats, Software Agents, Robots, Adaptive Systems
Evolution of functional specialization in a morphologically homogeneous robot
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
The Cognitive Body: From Dynamic Modulation to Anticipation
Anticipatory Behavior in Adaptive Learning Systems
How robot morphology and training order affect the learning of multiple behaviors
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Fitness Space Structure of a Neuromechanical System
Adaptive Behavior - Animals, Animats, Software Agents, Robots, Adaptive Systems
Guarding against premature convergence while accelerating evolutionary search
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Flexible and multistable pattern generation by evolving constrained plastic neurocontrollers
Adaptive Behavior - Animals, Animats, Software Agents, Robots, Adaptive Systems
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Evolving complete robots with CPPN-NEAT: the utility of recurrent connections
Proceedings of the 13th annual conference on Genetic and evolutionary computation
A species-based approach to brain-body co-evolution of modular robots
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
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A fundamental challenge for any general theory of neural circuits is how to characterize the structure of the space of all possible circuits over a given model neuron. As a first step in this direction, this letter begins a systematic study of the global parameter space structure of continuous-time recurrent neural networks (CTRNNs), a class of neural models that is simple but dynamically universal. First, we explicitly compute the local bifurcation manifolds of CTRNNs. We then visualize the structure of these manifolds in net input space for small circuits. These visualizations reveal a set of extremal saddle node bifurcation manifolds that divide CTRNN parameter space into regions of dynamics with different effective dimensionality. Next, we completely characterize the combinatorics and geometry of an asymptotically exact approximation to these regions for circuits of arbitrary size. Finally, we show how these regions can be used to calculate estimates of the probability of encountering different kinds of dynamics in CTRNN parameter space.