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Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Necessary and sufficient conditions are given for the asymptotic stability and instability of a two-dimensional incommensurate order autonomous linear system, which consists of a differential equation with a Caputo-type fractional order…
We investigate the scalar autonomous equation with two discrete delays $$ \dot{x}(t)=f(x(t),x(t-r),x(t-\sigma)), $$ where $f:\mathbb{R}^3\rightarrow \mathbb{R}$ is a continuously differentiable non-linear function such that $f(0,0,0)=0$. It…
For the reduced two-dimensional Belousov-Zhabotinsky slow-fast differential system, the known results are the existence of one limit cycle and its stability for particular values of the parameters. Here, we characterize all dynamics of this…
We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider in particular a…
Dynamical properties of ultradiscrete Hopf bifurcation, similar to those of the standard Hopf bifurcation, are discussed by proposing a simple model of ultradiscrete equations with max-plus algebra. In ultradiscrete Hopf bifurcation, limit…
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…
The spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
Recent studies of biological, chemical, and physical pattern-forming systems have started to go beyond the classic `near onset' and `far from equilibrium' theories for homogeneous systems to include the effects of spatial heterogeneities.…
In the context of a spatially extended model for the electrical activity in a pituitary lactotroph cell line, we establish that two delayed bifurcation phenomena from ODEs ---folded node canards and slow passage through Hopf bifurcations---…
Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…
This work examines the global dynamics of classical solutions of a two-stage (juvenile-adult) reaction-diffusion population model in time-periodic and spatially heterogeneous environments. It is shown that the sign of the principal…
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two regimes are studied in detail. In the first, the homogeneous…
A ferrofluid droplet confined in a Hele-Shaw cell can be deformed into a stably spinning ``gear,'' using crossed magnetic fields. Previously, fully nonlinear simulation revealed that the spinning gear emerges as a stable traveling wave…
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its…
A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…
We study nonstationary intermittent dynamical systems, such as compositions of a (deterministic) sequence of Pomeau-Manneville maps. We prove two main results: sharp bounds on memory loss, including the "unexpected" faster rate for a large…
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in…
We develop and analyze mathematical models for residential burglary that incorporates police deployment through a delayed feedback mechanism. Motivated by empirical observations from publicly available crime and policing data, we extend a…
We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…