Related papers: Controlling complex rhythms: A hierarchical approa…
Cognitive control is a suite of processes that helps individuals pursue goals despite resistance or uncertainty about what to do. Although cognitive control has been extensively studied as a dynamic feedback loop of perception, valuation,…
Utilizing a paradigmatic model for the motion of interacting self-propelled particles, we demonstrate that local accelerations at the level of individual particles can drive transitions between different collective dynamics, leading to a…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We study limit cycles in piecewise complex systems with switching manifold $\mathbb{S}^1$. Using M\"obius transformations we establish an equivalence between circular and straight-line discontinuities that preserves periods, stability, and…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest…
Mobile manipulators are envisioned to serve more complex roles in people's everyday lives. With recent breakthroughs in large language models, task planners have become better at translating human verbal instructions into a sequence of…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a…
The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles…
We investigate how dynamical decoupling methods may be used to manipulate the time evolution of quantum many-body systems. These methods consist of sequences of external control operations designed to induce a desired dynamics. The systems…
Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g. animal vasculature, depends on periodic…
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with…
Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map…