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The natural impedance, or dynamic relationship between force and motion, of a human operator can determine the stability of exoskeletons that use interaction-torque feedback to amplify human strength. While human impedance is typically…
Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a…
A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a…
Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in…
A general FitzHugh-Rinzel model, able to describe several neuronal phenomena, is considered. Linear stability and Hopf bifurcations are investigated by means of the spectral equation for the ternary autonomous dynamical system and the…
Platelet adhesion and aggregation are essential for primary hemostasis, forming a clot that quickly stops initial bleeding. Despite this critical role, the dynamic interactions of platelet receptors with exposed collagen and von Willebrand…
We describe a new complex system model of an evolving production economy. This model is the simplest we can envisage which incorporates the new observation that the rate of an economic production process depends only on the minimum of its…
An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by…
We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. The mechanistic model is an ordinary differential…
We analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors…
We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values…
Since the seminal work by H.L.F. Helmholtz in 1863, to understand the basic principles of hearing has been a great, but still unresolved, challenge for physicists. Some time ago, it has been pointed out (Egu\'{\i}luz et al., Phys. Rev.…
In this work, we propose a dynamical systems perspective on the modeling of sepsis and its organ-damaging consequences. We develop a functional two-layer network model for sepsis based upon the interaction of parenchymal cells and immune…
Goodwin's model is a cornerstone in the study of dynamical systems within macroeconomics, explaining the interaction between employment ratio and wage share in a closed economy. Analogous to predator-prey dynamics in mathematical economics,…
The functional diversity in factors identified in association with non-alcoholic fatty liver disease (NAFLD) necessitates the utilization of holistic approaches to investigate the network properties of NAFLD pathogenesis. We describe the…
Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context…
A model for the transmission dynamics of gonorrhoea with control incorporating passive immunity is formulated. We show that introduction of treatment or control parameters leads to transcritical bifurcation. The backward bifurcation…
We consider a broad class of second-order dynamical systems and study the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. We prove a monotonic effect of damping on the hyperbolicity…
In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize the…
Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…