A unified tensor framework models higher-order Markov chains with memory via an even-order paired tensor linking folded and unfolded dynamics, with approximation to low-dimensional nonlinear systems and application to hypergraph random walks.
An sis diffusion process with direct and indirect spreading on a hypergraph,
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Under a tensor generalized detailed-balance condition, tensor-coupled flow-conservation systems on hypergraphs have a unique equilibrium with global asymptotic stability via an entropy Lyapunov function, plus sensitivity bounds and local ISS linking spectral gap to robustness.
A structure-preserving linear feedback for ODECO homogeneous polynomial systems yields explicit closed-loop trajectories, convergence thresholds, and sharp ROA characterizations.
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Markov Chains and Random Walks with Memory on Hypergraphs: A Tensor-Based Approach
A unified tensor framework models higher-order Markov chains with memory via an even-order paired tensor linking folded and unfolded dynamics, with approximation to low-dimensional nonlinear systems and application to hypergraph random walks.
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Stability and Robustness of Tensor-Coupled Flow-Conservation Dynamical Systems on Hypergraphs
Under a tensor generalized detailed-balance condition, tensor-coupled flow-conservation systems on hypergraphs have a unique equilibrium with global asymptotic stability via an entropy Lyapunov function, plus sensitivity bounds and local ISS linking spectral gap to robustness.
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Linear Feedback Controller for Homogeneous Polynomial Systems
A structure-preserving linear feedback for ODECO homogeneous polynomial systems yields explicit closed-loop trajectories, convergence thresholds, and sharp ROA characterizations.