165 papers
This paper establishes an optimal result for the differentiable normal linearization of partially hyperbolic diffeomorphisms by constructing a local conjugacy that is on the center manifold to achieve Takens' normal form without requiring non-resonant conditions, overcoming decoupling difficulties through a novel semi-decoupling method and advanced extension techniques.
This paper introduces a novel construction of local Morse homology to compute the homology of critical points in the Lagrange problem, thereby proving that linear critical points are either saddle points or degenerate, refining the previous conclusion that they must be saddle points if non-degenerate.
This paper presents a unified framework that proves the equivalence of variational, Green's function, and characteristic-based methods for constructing reproducing kernels, enabling a data-driven, mesh-free approach to learning kernels that accurately approximate Koopman eigenfunctions and solve various linear transport equations.
This paper investigates rate-induced tipping in a moving habitat using a non-autonomous reaction-diffusion model, demonstrating that populations face extinction if the habitat's displacement rate exceeds a unique critical threshold, a phenomenon analytically characterized by heteroclinic connections between stable and unstable states.
This paper analyzes a normalized two-dimensional competitive Lotka-Volterra model of state-society interaction, demonstrating that as parameters approach a critical coexistence threshold, the system exhibits slow convergence and prolonged transient dynamics organized within a narrow corridor around a balance manifold, even in the absence of bistability.
This paper reformulates Constructal evolution as a nonsmooth dynamical system governed by Filippov differential inclusions, proving that irreversible transport constraints and resistance dissipation guarantee the existence, uniqueness, and global exponential stability of optimal flow architectures without relying on static optimization.
This paper introduces a geometric framework of Covariant Multi-Scale Negative Coupling on dynamic Riemannian manifolds to counteract dimensional reduction in dissipative PDEs, theoretically proving the finite dimensionality of global attractors while numerically validating the mechanism's ability to stabilize high-dimensional structural complexity against macroscopic dissipation.
This paper proposes weaker constraints on filters for group convolutional neural networks that reduce the required number of nodes while resolving incompatibilities with non-compact stabilizers and generalizing results to non-transitive group actions and non-unimodular groups.
This paper presents a fast, scalable method that combines deep learning with Dynamic Input Conductances (DICs) to reconstruct diverse, degenerate populations of conductance-based neuron models directly from spike times, effectively bridging experimental recordings and mechanistic biophysical parameters.
This paper demonstrates that gating mechanisms in recurrent neural networks act as data-driven preconditioners that couple state-space time-scales with parameter-space dynamics, inducing lag-dependent and anisotropic effective learning rates that complement optimizer-driven adaptivity to enhance trainability.
The paper introduces NN-OpInf, a structure-preserving, composable neural network framework for non-intrusive reduced-order modeling that outperforms traditional polynomial methods in accuracy and stability for systems with non-polynomial nonlinearities, albeit at the cost of higher computational training requirements.
This paper proposes a low-energy, low-thrust trajectory design for a mission touring Saturn's inner large moons (Rhea, Dione, Tethys, Enceladus, and Mimas) that utilizes J2-perturbed three-body dynamics and invariant manifolds to achieve full surface coverage while minimizing fuel consumption and maximizing observation time compared to traditional flyby missions.
This paper establishes delay-independent stability conditions for a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient through linearization, characteristic equations, and bifurcation theory, with results validated by numerical simulations and stability diagrams.
This paper establishes a cohomological criterion for decomposing Borel graphs, analogous to Dunwoody's work on group accessibility, and applies it to prove that Borel graphs with uniformly bounded degrees and cohomological dimension one are Lipschitz equivalent to acyclic graphs, thereby providing a new proof of a result by Chen et al. regarding graphs with tree-like components.
This paper establishes the existence of Wilton ripple solutions for the Kawahara equation for all integer values of by employing a Lyapunov-Schmidt reduction, thereby extending previous results that were limited to the specific case of .
This paper characterizes the solution spaces of perturbed linear stochastic Volterra equations in discrete and continuous time, establishing that while -summable perturbations are necessary and sufficient for almost sure -summability in the discrete case, the continuous case allows for almost sure -integrability even with non-integrable perturbations, a result proven via discretization and extended to analyze asymptotic convergence and broader functional differential equations.
This paper establishes that factors of smooth words are f-smooth and advances Sing's conjecture on their complexity by proving the asymptotic growth rate for even alphabets, confirming the lower bound for all binary alphabets, and improving the upper bound for odd alphabets.
This study mathematically analyzes a chemostat model of obligate mutualism to demonstrate that incorporating mortality significantly enriches the system's dynamical repertoire, enabling complex phenomena such as multistability, oscillatory coexistence, and diverse bifurcations that are absent in mortality-free scenarios.
This paper develops a theory of discrete averaging for discrete-time dynamical systems that utilizes weighted trajectory averages to directly approximate autonomous vector fields, thereby eliminating intermediate steps of classical averaging to provide explicit error bounds and establish the validity of adiabatic invariants for near-identity maps and resonant fixed points.
This paper establishes sufficient conditions, based on the admissibility of function classes and a smallness integrability condition, for the preservation of nonuniform exponential dichotomies under nonlocal perturbations.