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Sea surface temperature (SST) variability plays a key role in the global weather and climate system, with phenomena such as El Ni\~{n}o-Southern Oscillation regarded as a major source of interannual climate variability at the global scale.…
The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
The variability of Indo-Pacific SST on seasonal to multidecadal timescales is investigated using a recently introduced technique called nonlinear Laplacian spectral analysis (NLSA). Through this technique, drawbacks associated with ad hoc…
Drought is a costly natural hazard, many aspects of which remain poorly understood. It has many contributory factors, driving its outset, duration, and severity, including land surface, anthropogenic activities, and, most importantly,…
The El Ni\~no Southern Oscillation (ENSO) is the strongest driver of year-to-year variations of the global climate and can lead to extreme weather conditions and disasters in various regions around the world. Here, we review two different…
In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of…
We study parameter estimation for the two state model which describes the balance equation for carbon dioxide and oxygen in human respiratory system. These are nonlinear parameter dependent and because of the transport delay in the…
The southern oscillation index (SOI) is a characteristic of the El Nino phenomenon. SOI monthly averaged data is analyzed for the time interval 1866-2000. The tail of the cumulative distribution of the fluctuations of SOI signal is studied…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal…
In this paper, we extend the demographic eco-evolutionary game approach, based on explicit birth and death dynamics instead of abstract "fitness" interpreted as an abstract "Malthusian parameter", by the introduction of the delay resulting…
We study a scalar, first-order delay differential equation (DDE) with instantaneous and state-dependent delayed feedback, which itself may be delayed. The state dependence introduces nonlinearity into an otherwise linear system. We…
Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network…
We begin by providing observational evidence that the probability of encountering very high and very low annual tropical rainfall has increased significantly in the recent decade (1998-present) as compared to the preceding warming era…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…
We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control…