Two coupled systems with simultaneous saddle-node bifurcations require four parameters for generic unfolding, producing complex local and global bifurcations including novel codimension-two types, together with new numerical continuation techniques for tracking them.
Co-evolutionary dynamics for two adaptively coupled Theta neurons
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Generalized saddle-node ghosts are defined for higher-dimensional systems with algorithms to detect ghost attractors, channels, and cycles, implemented in the PyGhostID Python package.
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Local interaction of two systems with saddle-node bifurcations: mutualistic and mixed cases
Two coupled systems with simultaneous saddle-node bifurcations require four parameters for generic unfolding, producing complex local and global bifurcations including novel codimension-two types, together with new numerical continuation techniques for tracking them.
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Generalized saddle-node ghosts and their composite structures in dynamical systems
Generalized saddle-node ghosts are defined for higher-dimensional systems with algorithms to detect ghost attractors, channels, and cycles, implemented in the PyGhostID Python package.