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Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring
This paper presents a new computational method for forward uncertainty quantification (UQ) analyses on large-scale structural systems in the presence...
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Non-intrusive polynomial chaos expansion for robust topology optimization of truss-like continuum under random loads
This paper dedicates to presenting an uncertainty analysis framework for robust topology optimization (RTO) based on truss-like material model that...
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Discrete superior dynamics of a generalized chaotic system
In the past few decades, the discrete dynamics of difference maps have attained the remarkable attention of researchers owing to their incredible...
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Multifractal Analysis of Local Polynomial Entropies
In this paper, we introduce the Bowen polynomial entropy and study the multifractal spectrum of the local polynomial entropies for arbitrary Borel...
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Advanced computational technique based on kriging and Polynomial Chaos Expansion for structural stability of mechanical systems with uncertainties
In this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the...
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Uncertainty Quantification of Stochastic Epidemic SIR Models Using B-spline Polynomial Chaos
Real-life epidemic situations are modeled using systems of differential equations (DEs) by considering deterministic parameters. However, in reality,...
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Controlling Chaos in 3D Porous Media in the Presence of Orientation Effect
AbstractThe influence of orientation on the control of chaotic behaviors of the system in a porous medium is studied in this article based on the...
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A splitting/polynomial chaos expansion approach for stochastic evolution equations
In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution...
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Dynamics of Predator–Prey Model Based on Fear Effect with Bifurcation Analysis and Chaos Control
Recent studies on terrestrial vertebrates have unveiled a correlation between fear of predators and a reduction in anti-predator defenses, leading to...
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Root location for the characteristic polynomial of a Fibonacci type sequence
We analyse the roots of the polynomial x n − px n −1 − qx − 1 for p ≽ q ≽ 1. This is the characteristic polynomial of the recurrence relation F k,p,q ( n ) = pF...
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Exploring dynamics of plant–herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response
In this study, we examine the plant–herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the...
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Parameter Identification of Fractional Order Partial Differential Equation Model Based on Polynomial–Fourier Method
Parameter identification plays a crucial role in the study of dynamics for fractional order structural models. This article introduces an innovative...
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Topological Entropy of Generalized Bunimovich Stadium Billiards
We estimate from below the topological entropy of the generalized Bunimovich stadium billiards. We do it for long billiard tables, and find the limit...
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Sharp uniform-in-time propagation of chaos
We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions...
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Generalized gradient structures for measure-valued population dynamics and their large-population limit
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in...
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Sparse Polynomial Approximations for Affine Parametric Saddle Point Problems
In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems, including...
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Limit cycles of multi-parameter polynomial dynamical systems
This is an overview of our recent works on the global bifurcation analysis of multi-parameter polynomial dynamical systems. In particular, using our...
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Numerical Experiments and Visualization of Chaos
The visualization of orbits and attractors of chaotic systems is a process that has been in progress for some time. Advances in computation, both in...