Related papers: Taming Explosive Growth through Dynamic Random Lin…
Inhibitory neurons play a crucial role in maintaining persistent neuronal activity. Although connected extensively through electrical synapses (gap-junctions), these neurons also exhibit interactions through chemical synapses in certain…
We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed…
We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size…
We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform…
We investigate collective synchronous behaviors in random complex networks of limit-cycle oscillators with the non-identical asymmetric coupling scheme, and find a uniform coupling criticality of collective synchronization which is…
We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with $m$ random interactions to older ones. Each constitutive element in the model stays either active or is temporarily…
Controlling growth via cell division is crucial in the development of higher organisms, and yet the mechanisms through which this is achieved, e.g., in epithelial tissue, is not yet fully understood. We show that by coupling the cell cycle…
Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria…
We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…
Understanding the global dynamical behaviour of a network of coupled oscillators has been a topic of immense research in many fields of science and engineering. Various factors govern the resulting dynamical behaviour of such networks,…
We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional…
There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of…
We leverage data-driven model discovery methods to determine the governing equations for the emergent behavior of heterogeneous networked dynamical systems. Specifically, we consider networks of coupled nonlinear oscillators whose…
We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
We investigate states of enhanced activity in a biological neuronal network composed of pulse-coupled oscillators. The synaptic couplings between the neurons are dynamic, modeling spike time dependent plasticity. The network exhibits…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range…