arXiv subjects

Kalel L. Rossi

Publications and source records attributed to Kalel L. Rossi.

6 recordsLinked to original sources

arXiv2026

Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure

We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronization and promote phase-locked patterns, including states with uniform phase gradients and more complex combinations of these modes. Yet, how connectivity and phase-delays jointly determine which states the network selects remains unclear. Here, we show that the spectrum of a composite matrix, which combines connectivity and phase-delays, governs not only the linear stability of the network's collective states but also their basin sizes. This, in turn, enables analytical estimates of basin size of phase-locked states for individual networks from connectivity and phase-delays alone. Applying this framework to nonlocal and global networks, including cases with random phase-delays, we uncover multistability and strong asymmetries in basin sizes, revealing chiral dynamics that conventional stability analysis cannot detect.

nlin.AO↗

arXiv2026

Delay coordinates synchronization and induces abrupt transition in excitable networks

Neuronal communication is inherently time-delayed, due to the finite speed of signal propagation. Although often considered challenging or disruptive, such time delays can also endow neural circuits with useful capabilities. Here, we show that delays in excitatory connections between excitable neurons coordinate their synchronization patterns by creating self-sustained oscillations that may be out-of-phase or in-phase. The emergence of these oscillations leads to an abrupt, explosive, transition to in-phase synchronized regimes due to small changes in connection strength or time-delay. We describe the mechanism underlying these phenomena as an interaction between the neuron's excitable dynamics and the delay in signal transmission, explaining many aspects of how the oscillations emerge. We show this phenomenon in different network connectivities, neuronal models, with and without excitation, with and without noise, highlighting the generality of the mechanism.

q-bio.NC↗

arXiv2026

Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks

We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through a nonlinear coordinate transformation. Here, we derive an exact analytical expression for the network's time-dependent maximum Lyapunov exponent (MLE). We demonstrate, both numerically and analytically, that the network exhibits positive MLEs during the transients that are useful for computation. Our framework enables algebraic manipulation of transient lifetimes through network connectivity and initial conditions, providing a rigorous theoretical foundation for understanding and controlling computation with transients.

nlin.CD↗

arXiv2024

Transients versus network interactions give rise to multistability through trapping mechanism

In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients that give rise to multistability from such interplay remain poorly understood. In a network of coupled excitable units, we show that this interplay generating multistability occurs through a competition between the units' transient dynamics and their coupling. Specifically, the diffusive coupling between the units manages to reinject them in the excitability region of their individual state space and effectively trap them there. We show that this trapping mechanism leads to the coexistence of multiple types of oscillations: periodic, quasiperiodic, and even chaotic, although the units separately do not oscillate. Interestingly, we show that the attractors emerge through different types of bifurcations - in particular, the periodic attractors emerge through either saddle-node of limit cycles bifurcations or homoclinic bifurcations - but in all cases the reinjection mechanism is present.

math.DS↗

arXiv2024

Dynamical properties and mechanisms of metastability: a perspective in neuroscience

Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this Perspective, we discuss metastability from the point of view of dynamical systems theory. We extract from the literature a very simple but general definition through the concept of metastable regimes as long-lived but transient epochs of activity with unique dynamical properties. This definition serves as an umbrella term that encompasses formulations from other works, and readily connects to concepts from dynamical systems theory. This allows us to examine general dynamical properties of metastable regimes, propose in a didactic manner several dynamics-based mechanisms that generate them, and discuss a theoretical tool to characterize them quantitatively. This perspective leads to insights that help to address issues debated in the literature and also suggest pathways for future research.

q-bio.NC↗

arXiv2022

Small changes at single nodes can shift global network dynamics

Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics, particularly different synchronization patterns, is crucial - or may be undesired - for instance in power grids, where disruptions to synchronization may lead to blackouts. In this work, we show that the dynamics of networks of phase oscillators can acquire a very large and complex sensitivity to changes made in either their units' parameters or in their connections - even modifications made to a parameter of a single unit can radically alter the global dynamics of the network in an unpredictable manner. As a consequence, each modification leads to a different path to phase synchronization manifested as large fluctuations along that path. This dynamical malleability occurs over a wide parameter region, around the network's two transitions to phase synchronization. One transition is induced by increasing the coupling strength between the units, and another is induced by increasing the prevalence of long-range connections. Specifically, we study Kuramoto phase oscillators connected under either Watts-Strogatz or distance-dependent topologies to analyze the statistical properties of the fluctuations along the paths to phase synchrony. We argue that this increase in the dynamical malleability is a general phenomenon, as suggested by both previous studies and the theory of phase transitions.

math.DS↗