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Attractor Dynamics in Feedforward Neural Networks
Neural Computation, 2000 We study the probabilistic generative models parameterized by feedfor-ward neural networks. An attractor dynamics for probabilistic inference in these models is derived from a mean field approximation for large, layered sigmoidal networks. Fixed points of the dynamics correspond to solutions of the mean field equations, which relate the statistics of ...
Lawrence K. Saul, Michael I. Jordan
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On boundaries of attractors in dynamical systems
Communications in Nonlinear Science and Numerical Simulation, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nitha Niralda P. C +2 more
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Attractor Selection in Chaotic Dynamics
Physical Review Letters, 2005For different settings of a control parameter, a chaotic system can go from a region with two separate stable attractors (generalized bistability) to a crisis where a chaotic attractor expands, colliding with an unstable orbit. In the bistable regime jumps between independent attractors are mediated by external perturbations; above the crisis, the ...
Meucci R +3 more
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Controlling Dynamics of Hidden Attractors
International Journal of Bifurcation and Chaos, 2015Amplitude death (AD) in hidden attractors is attained with a scheme of linear augmentation. This linear control scheme is capable of stabilizing the system to a fixed point state even when the original system does not have any fixed point. Depending on the control parameter, different routes to AD such as boundary crises and Hopf bifurcation are ...
Sharma, Pooja Rani +5 more
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ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS
International Journal of Bifurcation and Chaos, 2001We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.
Peter W. Bates, Kening Lu, Bixiang Wang
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Invasion dynamics and attractor inheritance
Journal of Mathematical Biology, 2002We study the dynamics of a population of residents that is being invaded by an initially rare mutant. We show that under relatively mild conditions the sum of the mutant and resident population sizes stays arbitrarily close to the initial attractor of the monomorphic resident population whenever the mutant has a strategy sufficiently similar to that of
Geritz, S. A. H. +3 more
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The “hidden” dynamics of the Rössler attractor
Physica D: Nonlinear Phenomena, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maris, Dimitris T., Goussis, Dimitris A.
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DYNAMICAL ANALYSIS OF A NEW CHAOTIC ATTRACTOR
International Journal of Bifurcation and Chaos, 2002Dynamical behaviors of a new chaotic attractor is investigated in this paper. Some basic properties, bifurcations, routes to chaos, and periodic windows of the new system are studied either analytically or numerically. Meanwhile, the transition between the Lorenz attractor and Chen's attractor through the new system is explored.
Jinhu Lü 0001 +2 more
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Attractor-like Dynamics in the Subicular Complex
The Journal of Neuroscience, 2022Distinct computations are performed at multiple brain regions during the encoding of spatial environments. Neural representations in the hippocampal, entorhinal, and head direction (HD) networks during spatial navigation have been clearly documented, while the representational properties of the subicular complex (SC) are relatively underexplored ...
Apoorv Sharma +2 more
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Attractors and Democratic Dynamics
Science, 2009Cellular transcription networks are conceptualized as distributed control systems that regulate gene expression.
Yaneer Bar-Yam +2 more
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