相关论文: Effective Reduced Models from Delay Differential E…
We present a computational method for studying transverse homoclinic orbits for periodic solutions of delay differential equations, a phenomenon that we refer to as the \emph{Poincar\'{e} scenario}. The strategy is geometric in nature, and…
Periodic orbits and associated bifurcations of singularly perturbed state-dependent delay differential equations (DDEs) are studied when the profiles of the periodic orbits contain jump discontinuities in the singular limit. A definition of…
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…
Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of the nature in the…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs…
We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…
We study a class of multi-parameter three-dimensional systems of ordinary differential equations that exhibit dynamics on three distinct timescales. We apply geometric singular perturbation theory to explore the dependence of the geometry…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
Multivariate time series forecasting plays a crucial role in various real-world applications. Significant efforts have been made to integrate advanced network architectures and training strategies that enhance the capture of temporal…
The El Ni\~no Southern Oscillation (ENSO) is the most important driver of interannual global climate variability and can trigger extreme weather events and disasters in various parts of the globe. Depending on the region of maximal warming,…
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…
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…
While deep-learning models have demonstrated skillful El Ni\~no Southern Oscillation (ENSO) forecasts up to one year in advance, they are predominantly trained on climate model simulations that provide thousands of years of training data at…
Predicting sea surface temperature (SST) within the El Ni\~no-Southern Oscillation (ENSO) region has been extensively studied due to its significant influence on global temperature and precipitation patterns. Statistical models such as…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…
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…
The El Ni\~no Southern Oscillation (ENSO) is the dominant driver of interannual global climate variability and can lead to extreme weather events such as droughts or flooding. Recently, we have developed several statistical approaches for…