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A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor…
Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called…
In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir…
Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be…
Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can…
We evaluate the mutual information between the input and the output of a two layer network in the case of a noisy and non-linear analogue channel. In the case where the non-linearity is small with respect to the variability in the noise, we…
In a complex system, perturbations propagate by following paths on the network of interactions among the system's units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very…
Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatio-temporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations…
Behavioral changes in animals and humans, as a consequence of an error or a verbal instruction, can be extremely rapid. Improvement in behavioral performances are usually associated in machine learning and reinforcement learning to synaptic…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce…
Many biological systems dynamically rearrange their components through a sequence of configurations in order to perform their functions. Such dynamic processes have been studied using network models that sequentially retrieve a set of…
We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external signal inputs. Particular emphasis is…
Achieving precise synchronisation between transmitters and receivers is particularly challenging in diffusive molecular communication environments. To this end, point-to-point molecular communication system design is examined wherein…
A coupled map is suggested to investigate various spatial or temporal designs in biology: Several cells (or tissues) in an organ are considered as connected to each other in terms of some molecular diffusions or electrical potential…
Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of…
Signal transduction in biological cells is effected by signaling pathways that typically include multiple feedback loops. Here we analyze information transfer through a prototypical signaling module with biochemical feedback. The module…