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In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call the radial
Externí odkaz:
http://arxiv.org/abs/2409.00668
Autor:
Nakai, Kengo, Saiki, Yoshitaka
In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully reconstruct th
Externí odkaz:
http://arxiv.org/abs/2407.06229
Autor:
Jeffrey, Mike R
A practical method was proposed recently for finding local bifurcation points in an n-dimensional vector field F by seeking their 'underlying catastrophes'. Here we apply the idea to the homogeneous steady states of a partial differential equation as
Externí odkaz:
http://arxiv.org/abs/2310.14818
Autor:
Jeffrey, Mike R.
Publikováno v:
J. Phys. A: Math. Theor. 55 464006 (2022)
Practical conditions are given here for finding and classifying high codimension intersection points of $n$ hypersurfaces in $n$ dimensions. By interpreting those hypersurfaces as the nullclines of a vector field in $\mathbb R^n$, we broaden the conc
Externí odkaz:
http://arxiv.org/abs/2310.14813
Autor:
Roy, Shashank Kumar, Apte, Amit
Computing Lyapunov vectors from partial and noisy observations is a challenging problem. We propose a method using data assimilation to approximate the Lyapunov vectors using the estimate of the underlying trajectory obtained from the filter mean. We
Externí odkaz:
http://arxiv.org/abs/2308.11465
In our previous study (N. Tsutsumi, K. Nakai and Y. Saiki (2022)) we proposed a method of constructing a system of differential equations of chaotic behavior only from observable deterministic time series, which we will call radial function-based reg
Externí odkaz:
http://arxiv.org/abs/2308.12382
Epidemiological models are an important tool in coping with epidemics, as they offer a forecast, even if often simplistic, of the behavior of the disease in the population. This allows responsible health agencies to organize themselves and adopt stra
Externí odkaz:
http://arxiv.org/abs/2307.14400
Publikováno v:
Journal of Nonlinear Science, 34:77, 2024
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical phenomena,
Externí odkaz:
http://arxiv.org/abs/2305.04277
The COVID-19 epidemic has been spreading around the world for nearly three years, and asymptomatic infections have exacerbated the spread of the epidemic. To evaluate the role of asymptomatic infections in the spread of the epidemic, we develop mathe
Externí odkaz:
http://arxiv.org/abs/2210.13114
Autor:
Jacob, Justin, Khaneja, Navin
This paper presents the control and stabilization of the rotary inverted pendulum based on a general controller scheme. The proposed scheme has its foundation in classical control theory, and the importance of an integrator in disturbance rejection i
Externí odkaz:
http://arxiv.org/abs/2209.01668