Related papers: Controlling complex rhythms: A hierarchical approa…

Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…

Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work…

The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…

The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic…

Hierarchical dynamics in glass-forming systems span multiple timescales, from fast vibrations to slow structural rearrangements, appearing in both supercooled fluids and glassy states. Understanding how these diverse processes interact…

Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…

Although the set of permutation symmetries of a complex network can be very large, few of the symmetries give rise to stable synchronous patterns. Here we present a new framework and develop techniques for controlling synchronization…

Small inhibitory neuronal circuits have long been identified as key neuronal motifs to generate and modulate the coexisting rhythms of various motor functions. Our paper highlights the role of a cellular switching mechanism to orchestrate…

This paper proposes an approach to addresses the control challenges posed by a fault-induced uncertainty in both the dynamics and control input effectiveness of a class of hierarchical nonlinear systems in which the high-level dynamics is…

We investigate the sensorimotor loop of simple robots simulated within the LPZRobots environment from the point of view of dynamical systems theory. For a robot with a cylindrical shaped body and an actuator controlled by a single…

Predictively steering self-organising systems with hierarchical structure toward intended outcomes across widely separated dynamical scales remains a fundamental challenge. Despite decades of progress, hierarchy remains a descriptive…

Brain functions require both segregated processing of information in specialized circuits, as well as integration across circuits to perform high-level information processing. One possible way to implement these seemingly opposing demands…

Flexible modulation of temporal dynamics in neural sequences underlies many cognitive processes. For instance, we can adaptively change the speed of motor sequences and speech. While such flexibility is influenced by various factors such as…

We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each…

We demonstrate that strongly asymmetric limit cycles can be observed in the system of three identical ring oscillators (3-gene networks known as Repressilators) globally coupled by signal molecule diffusion added to the model in a way like…

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…

The heterogeneity among interacting dynamical systems or variations in the pattern of their interactions occur naturally in many real complex systems. Often they lead to partially synchronized states like chimeras or oscillation suppressed…

Changes in an animal's behavioral state, such as arousal and movements, induce {complex modulations of the baseline input currents to sensory areas, eliciting sensory modality-specific effects. A simple computational principle explaining…