Related papers: Chaotic dynamics of fractional Vallis system for E…
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…
This paper studies the chaotic behavior of hydrosphere and its influence on global weather and climate. We give mathematical arguments for the sea surface temperature (SST) to be unpredictable over the global ocean. The impact of SST…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
Anomalies during an El Nino are dominated by a single, irregularly oscillating, mode. Equatorial dynamics has been linked to delayed-oscillator models of this mode. Usually, the El Nino mode is regarded as an unstable mode of the coupled…
We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system.…
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of…
The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The…
We study the effect of parameter fluctuations on synchronization of a coupled chaotic system. The fluctuations to the parameter can be random or it can be a periodic modulation. For random fluctuations we introduce a new quantity, the…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
The shape and tails of partial distribution functions (PDF) for a climatological signal, i.e. the El Nino SOI and the turbulent nature of the ocean-atmosphere variability are linked through a model encompassing Tsallis nonextensive…
We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the…
One of the fundamental tasks in the study of dynamical systems is the discrimination between regular and chaotic behavior. Over the years several methods of chaos detection have been developed. Some of them, such as the construction of the…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
Complex networks have been used intensively to investigate the flow and dynamics of many natural systems including the climate system. Here, we develop a percolation based measure, the order parameter, to study and quantify climate…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
We describe a simple experimental implementation of the Malkus-Lorenz water wheel. We demonstrate that both chaotic and periodic behavior is found as wheel parameters are changed in agreement with predictions from the Lorenz model. We…
We investigate a low-dimensional slow-fast model to understand the dynamical origin of El Ni\~no-Southern Oscillation. A close inspection of the system dynamics using several bifurcation plots reveals that a sudden large expansion of the…