Related papers: A Nonhyperbolic Toy Model of Cochlear Dynamics
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Nonlinear dynamics clamp the amplitude of mechanical resonators driven into self-oscillation by optomechanical backaction. Here we overcome the conventional limits of self-oscillation amplitude by navigating the nonlinear dynamical…
The buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are…
A general form of a many-body Hamiltonian is considered, which includes an interacting fermionic sub-system coupled to non-interacting extended fermionic and bosonic systems. We show that the exact dynamics of the extended bosonic system…
This paper discusses the role of 2-D/3-D cochlear fluid hydrodynamics in the generation of the large nonlinear dynamical range of the basilar membrane (BM) and pressure response, in the decoupling between cochlear gain and tuning, and in…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
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The Duffing oscillator describes the dynamics of a mass suspended on a spring with position-dependent stiffness. The mass is assumed to experience a linear damping and a time-dependent external forcing. The model has been instrumental in…
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The modeling of the beating of cilia and flagella in fluids is a particularly active field of study, given the biological relevance of these organelles. Various mathematical models have been proposed to represent the nonlinear dynamics of…
For the hopping dynamics in a one-dimensional model, containing energy and barrier disorder, we determine the linear and nonlinear response to an external field for arbitrary external frequencies. The calculation is performed in analytical…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global…
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…
Nonlinear dynamics emerge through either nonlinear interactions between the variables or through nonlinearities imposed on their linear interactions. Their interactions can be conceptualized as modulations of input-output (I/O) functions,…
We consider the dissipative dynamics of a qubit coupled to a nonlinear oscillator (NO) embedded in an Ohmic environment. By treating the nonlinearity up to first order and applying Van Vleck perturbation theory up to second order in the…
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Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…