Related papers: An approximate threshold condition for a non-auton…

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no…

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…

The study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings, provided the system is large enough. Careful examination suggests that…

Dengue is a vector-borne disease and 40% of world population is at risk. Dengue transcends international borders and can be found in tropical and subtropical regions around the world, predominantly in urban and semi-urban areas. A model for…

This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the…

When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…

Common respiratory viruses cause seasonal epidemics in sequential patterns. The underlying mechanisms for this pattern have been debated for some time. For influenza, contenders include temperature, humidity, and vitamin D levels. While…

Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…

We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dengue fever is a vector-borne disease mostly endemic to tropical and subtropical countries that affect millions every year and is considered a significant burden for public health. Its geographic distribution makes it highly sensitive to…

The rampant phenomenon of overpopulation and the remarkable increase of human movements over the last decade have caused an aggressive re-emergence of dengue fever, which made it the subject of several research fields. In this regard,…

We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…

An SIRS epidemiological model for a vertically transmitted disease is discussed. We give a complete global analysis in terms of three explicit threshold parameters which respectively govern the existence and stability of an endemic…

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

The laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. Meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy…

We study a nonlinear coupled system of partial differential equations arising from thermo--reaction--phase models. The system combines a heat diffusion equation, temperature-dependent chemical reactions of Arrhenius type, and a phase…

To describe the nonequilibrium states of the system, a new thermodynamic parameter - system lifetime - is introduced. Statistical distributions that describe the behavior of energy and lifetime are recorded. Entropy and obtained…

We propose a variation of the GMS model of evolution of species. In this version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness mark, but in our variation, to each extinction event is…

We analyze a neural system which mimics a sensorial cortex, with different input characteristics, in presence of transmission delays. We propose a new measure to characterize collective behavior, based on the nonlinear extension of the…