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The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…
Linear thresholding systems have been used as a model of neural activation and have more recently been proposed as a model of gene activation. Deterministic linear thresholding systems can be turned into non-deterministic systems by the…
Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…
The paper describes the application of some numerical techniques to analyze and to characterize the observed dynamical behaviour of fluidized bed systems. The preliminary results showed clearly that the dynamics of the considered process…
We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…
Detection of critical slowing down (CSD) is the dominant avenue for anticipating critical transitions from noisy time-series data. Most commonly, changes in variance and lag-1 autocorrelation [AC(1)] are used as CSD indicators. However,…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using…
Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…