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Bifurcation and chaos in a discrete Holling–Tanner model with Beddington–DeAngelis functional response
The dynamics of a discrete Holling–Tanner model with Beddington–DeAngelis functional response is studied. The permanence and local stability of fixed...
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Analysis and control of the fractional chaotic Hopfield neural network
The fractional Hopfield neural network (HNN) model is studied here analyzing its symmetry, uniqueness of the solution, dissipativity, fixed points...
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Environmental Stochasticity Driving the Extinction of Top Predators in a Food Chain Chemostat Model
Understanding the process of extinction in natural populations is crucial for the preservation of ecosystem stability and biodiversity, both...
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Chaotic Time Series Prediction Using Random Fourier Feature Kernel Least Mean Square Algorithm with Adaptive Kernel Size
The random Fourier feature kernel least mean square (RFF-KLMS) algorithm provides a finite dimensional approximation to the kernel least mean square...
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The fractional-order Lorenz-type systems: A review
This paper deals with a survey of Lorenz-type systems. For the first time, a new classification of the fractional-order Lorenz-type systems was...
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Basic Concepts of Chaos Theory and Nonlinear Time-Series Analysis
We introduce the basic concepts and methods to formalize and analyze deterministic chaos, with links to fractal geometry. A chaotic dynamic is...
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The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps
This paper proposes three fractional discrete chaotic systems based on the Rulkov, Chang, and Zeraoulia-Sprott rational maps. The dynamics of the...
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Unfolding a Bykov Attractor: From an Attracting Torus to Strange Attractors
In this paper we present a comprehensive mechanism for the emergence of strange attractors in a two-parametric family of differential equations...
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Fractals via Self-Similar Group of Fisher Contractions
The fractal notion was unveiled by Mandelbrot in 1975, and a number of researchers continued to popularize the fractal theory. The chaotic structures...
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Reversibility, irreversibility, friction and nonequilibrium ensembles in N–S equations
Viscosity, as a physical property of fluids, reflects an average effect over a chaotic microscopic motion described by Hamiltonian equations. It is...
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On Partially Hyperbolic Diffeomorphisms and Regular Denjoy Type Homeomorphisms
In P. D. McSwiggen’s article, it was proposed Derived from Anosov type construction which leads to a partially hyperbolic diffeomorphism of the...
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Dimension of a Class of Intrinsically Transversal Solenoidal Attractors in High Dimensions
We study the fractal dimension of a class of solenoidal attractors in dimensions greater or equal than 3, proving that if the contraction is...
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Global attractors for a tropical climate model
This paper is devoted to the global attractors of the tropical climate model. We first establish the global well-posedness of the system. Then by...
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An Adaptive Data-Driven Reduced Order Model Based on Higher Order Dynamic Mode Decomposition
A new data-driven reduced order model is developed to efficiently simulate transient dynamics, with the aim at computing the final attractor. The...
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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...
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Design and Analysis of a Group of Correlative and Switchable Dual Memristor Hyperchaotic Systems
In this paper, a group of correlative and switchable dual memristor hyperchaotic systems consisting of three subsystems is constructed. The common...
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Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem
A generalization of the Suslov problem with changing parameters is considered. The physical interpretation is a Chaplygin sleigh moving on a sphere....
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A Novel Fractional-Order Cascade Tri-Neuron Hopfield Neural Network: Stability, Bifurcations, and Chaos
In this paper, we propose a novel Caputo-type fractional-order cascade tri-neuron Hopfield neural network (HNN) taking no connection between the...
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Limiting behaviour of non-autonomous Caputo-type time-delay systems and initial-time on the real number line
In many emerging scientific applications, the input of random initial time is often required for predicting and controlling the dynamics of...
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Random Attractor for Stochastic Hindmarsh–Rose Equations with Additive Noise
For stochastic Hindmarsh–Rose equations with additive noises in the study of neurodynamics, the longtime and global pullback dynamics on a...