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Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative…
Certain cellular processes take the form of activity pulses that can be interpreted in terms of noise-driven excitable dynamics. Here we present an overview of different gene circuit architectures that exhibit excitable pulses of protein…
Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in…
Cellular behavior is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have…
We show that oscillations are excited in a complex system under the influence of the external force, if the parameters of the system experience rapid change due to the changes in its internal structure. This excitation is collision-like and…
We investigate theoretically the dynamics of the system that consists of a cascade three-level emitter interacting with a single-mode resonator in the deep-strong-coupling regime. We show that the dynamical evolution of the system can only…
Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations of localized steady states in pattern-forming partial…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Genetically encoded regulatory circuits control biological function. A major focus of systems biology is to understand these circuits by establishing the relationship between specific structures and functions. Of special interest are…
Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…
Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…