适应与自组织系统

The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models…

We present a machine-learning method for data-driven synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems. Based on the phase autoencoder [Yawata {\it et al.}, Chaos {\bf 34}, 063111 (2024)], we map…

We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in…

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 investigate a simple nonequilibrium system with many interconnected, open subsystems, each exchanging a globally conserved resource with an external reserve. The system is represented by a random graph, where nodes…

These lectures are based on material which was presented in the 2025 Summer school at Funda\c{c}\~ao Getulio Vargas. The aim of this series is to introduce graduate students with a little background in the field of dynamical systems and…

Non-reciprocal interactions, where the influence of agent $i$ on $j$ differs from that of $j$ on $i$, are fundamental in active and living matter. Yet, most models implement such asymmetry phenomenologically. Here we show that…

We develop a unified, dynamical-systems narrative of the universe that traces a continuous chain of structure formation from the Big Bang to contemporary human societies and their artificial learning systems. Rather than treating cosmology,…

We introduce a frustration parameter $\alpha$ into the Vicsek-Kuramoto systems of self-propelled particles. While the system exhibits conventional synchronized states, such as global phase synchronization and swarming, for low frustration…

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger,…

Robustness and evolvability are essential properties to the evolution of biological networks. To determine if a biological network is robust and/or evolvable, it is required to compare its functions before and after mutations. However, this…

Self-organization can be broadly defined as the ability of a system to display ordered spatio-temporal patterns solely as the result of the interactions among the system components. Processes of this kind characterize both living and…

This study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, we demonstrate that intrinsic time…

Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…

We employ a thermodynamically consistent out-of-equilibrium continuum model to study the motion patterns of partially wetting liquid drops covered by autocatalytically reacting surfactants. When ambient chemostats feed a chemomechanical…

Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units.…

We focus on an interesting dissipative system found in a photonics system. In this dissipative system, we theoretically identified that robust causality is generated and as a result, it becomes possible to produce behavior that can be…

Self-organizing systems consume energy to generate internal order. The concept of thermodynamic efficiency, drawing from statistical physics and information theory, has previously been proposed to characterise a change in control parameter…

Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…

Agency is widely characterized as the capacity of a system to regulate its internal states toward self-generated goals, yet characterizing the functional basis of this autonomy requires a distinction between the system's own organization…