Related papers: Examining the evolution of phase-space elements fo…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the…
We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
A great deal of effort has been recently devoted to the study of dielectric relaxation processes in ferroelectric nematic liquid crystals, yet their interpretation remains unclear. In this work, we present the results of broadband…
Despite the relative simplicity of C. elegans, its locomotion machinery is not yet well understood. We focus on the generation of dorsoventral body bends. While central pattern generators are commonly involved in animal locomotion, their…
Abrupt changes in behavior can often be associated with changes in underlying behavioral states. When placed off food, the foraging behavior of C. elegans can be described as a change between an initial local-search behavior characterized…
Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar…
We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information…
Undulatory swimming is a widespread propulsion strategy adopted by many small-scale organisms including various single-cell eukaryotes and nematodes. In this work, we report a comprehensive study of undulatory locomotion of a finite…
Instabilities in 1D spatially extended systems are studied with the aid of both temporal and spatial Lyapunov exponents. A suitable representation of the spectra allows a compact description of all the possible disturbances in tangent…
Many dynamical systems found in biology, ranging from genetic circuits to the human brain to human social systems, are inherently computational. Although extensive research has explored their resulting functions and behaviors, the…
Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental…