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Properties of the response functions for a two-dimensional quartic oscillator are studied based on the diagonalization of the Hamiltonian in a large model space. In particular, response functions corresponding to a given momentum transfer…

Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…

Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…

One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…

This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…

We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe the regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show…

This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…

Delay is an inherent feature of genetic regulatory networks. It represents the time required for the assembly of functional regulator proteins. The protein production process is complex, as it includes transcription, translocation,…

In this paper, we are concerned with the state feedback stabilization of ODE-PDE cascade systems governed by a linear ordinary differential equation and the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to the…

The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…

Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…

The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…

We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with…

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…

Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…

Strong eastward jets at the equator have been observed in many planetary atmospheres and simulated in numerical models of varying complexity. However, the nature of the transition from a conventional state of the general circulation, with…

Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…