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A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase-amplitude reduction techniques, leveraging an analytical…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…
In this paper, we investigate the dynamical behaviors of a delayed lateral vibration model of footbridges proposed based on the facts that pedestrians will reduce their walking speed or stop walking when the response of the footbridge…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
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…
This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping.…
The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of systems with one-dimensional internal dynamics and with…
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…
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…
Spin masers are a prototype nonlinear dynamic system. They undergo a bifurcation at a critical amplification factor, transiting into a limit cycle phase characterized by a Larmor precession around the external bias magnetic field, thereby…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
We investigate a diffusive, stage-structured epidemic model with the maturation delay and freely-moving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than…
We consider the model of economic growth with time delayed investment function. Assuming the investment is time distributed we can use the linear chain trick technique to transform delay differential equation system to equivalent system of…
In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model…
We solve a simple model that supports a dynamic phase transition and show conditions for the existence of the transition. Using methods of large deviation theory we analytically compute the probability distribution for activity and entropy…
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one…
Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed…