Macroeconomic mathematical models are practical instruments structured to carry out theoretical analyses of macroeconomic developments. In this manuscript, the Caputo-like fractional operator of variable order is used to introduce and investigate the...
In this work, we recall some definitions on fractional calculus with discrete-time. Then, we introduce a discrete-time Hopfield neural network (D.T.H.N.N) with non-commensurate fractional variable-order (V.O) for three neurons. After that, phase-plot...
Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) wit...
The possibilities of micrometeorological resilience in urban contexts immersed in a basin geographical configuration are investigated. For this purpose, time series data with measurements of meteorological variables (temperature, magnitude of wind sp...
This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type...
Rehabilitation after anterior cruciate ligament reconstruction cannot be reduced to a linear, time-based sequence of protection, strength, and return to sport. Persistent asymmetries, quadriceps inhibition, and variable re-injury rates highlight that...
Up until now, studies of Kauffman network stability have focused on the conditions resulting from the structure of the network. Negative feedbacks have been modeled as ice (nodes that do not change their state) in an ordered phase but this blocks the...
The chaos-based optimization algorithm (COA) is a method to optimize possibly nonlinear complex functions of several variables by chaos search. The main innovation behind the chaos-based optimization algorithm is to generate chaotic trajectories by m...
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gib...
Standard correlation analysis is one of the frequently used methods in financial markets. However, this matrix can give erroneous results in the conditions of chaos, fractional systems, entropy, and complexity for the variables. In this study, we emp...
We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathe...
Four-dimensional chaotic systems have garnered significant attention due to their complex nonlinear dynamics, high-dimensional complexity, and wide range of applications in science and engineering. This paper proposes and investigates a novel four-di...
The new way of thinking science from Newtonian determinism to nonlinear unpredictability and the dawn of advanced computer science and technology can be summarized in the words of the theoretical physicist Michel Baranger, who, in 2000, said in a con...
A study was carried out in Santiago de Chile, located in a geographic basin, on the sustainability and diffusion of the recent SARS-CoV-2 pandemic. Hourly measurements were used (carried out for 3.25 years in seven communes of the city) to quantify t...
This paper studies a continuous Bertrand duopoly game model with two-stage delay. Our aim is to investigate the influence of delay and weight on the complex dynamic characteristics of the system. We obtain the bifurcation point of the system respect...
The earth’s surface is heated by the large-scale movement of air known as atmospheric circulation, which works in conjunction with ocean circulation. More than
Macroeconomic systems are increasingly characterized by fractal structures, entropy-generating processes, and chaotic dynamics that challenge the assumptions of traditional regression methods. The presence of self-similarity, fractal structure, and s...
We present a dynamical systems analysis of ion-acoustic waves in a forced plasma system, focusing on chaos, multistability, and stochastic sensitivity as functions of the Mach number. Both deterministic and stochastic versions of a reduced third-orde...
Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, bi...
Understanding complex systems requires analytical tools capable of covering nonlinear dynamics, structural complexity, and informational uncertainty simultaneously. In this context, chaos theory, fractal analysis, and entropy measures provide complem...
Fractional-order chaotic systems have emerged as powerful tools in secure communications and multimedia protection owing to their memory-dependent dynamics, large key spaces, and high sensitivity to initial conditions. However, most existing fraction...
This study investigates how non-ideal electromechanical actuation influences the emergence and modulation of complex dynamics in dissipative nonlinear systems. A hybrid four-dimensional model is formulated by coupling a continuous stirred tank reacto...
The paper presents an improved Komodo Mlipir Algorithm (KMA) with variable inertia weight and chaos mapping (VWCKMA). In contrast to the original Komodo Mlipir Algorithm (KMA), the chaotic sequence initialization population generated by Tent mapping...
To construct a chaotic system with complex characteristics and to improve the security of image data, a five-dimensional tri-valued memristor chaotic system with high complexity is innovatively constructed. Firstly, a pressure-controlled tri-valued m...
The concentration distribution of anthropocentric pollutants is favored by urban densification, affecting the micrometeorology in big cities. To examine this condition, chaos theory was applied to time series of measurements of urban meteorology and...
This study investigated urban water consumption complexity using chaos theory to improve forecasting performance to help optimize system management, reduce costs and improve reliability. The objectives of this study were to (1) investigate urban wate...
In this study, we develop a novel variable-order fractional extension of an eight-dimensional (8D) hyperchaotic differential equation system modeled via the Liouville–Caputo operator. Moving beyond constant fractional-order models, our system i...
As conventional computing architectures face fundamental physical limitations and the von Neumann bottleneck constrains computational efficiency, neuromorphic systems have emerged as a promising paradigm for next-generation information processing. Me...
Due to the security weaknesses of chaos-based pseudorandom number generators, in this paper, a new pseudorandom number generator (PRNG) based on mixing three-dimensional variables of a cat chaotic map is proposed. A uniformly distributed chaotic sequ...
This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and cha...
Modelling the Earth’s ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weathe...
This work investigates the complex dynamics of two novel Holling type II predator–prey (PP) models under the impact of climate change and controlled by the Caputo and Caputo–Fabrizio fractional operators. Here, Holling type II and static...
Complex-variable chaotic systems (CVCSs) have numerous advantages over real-variable chaotic systems in chaos communication due to their increased unpredictability, confidentiality, and the ease of implementation. Synchronization between the master a...
The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the c...
This article deals with the global existence and uniqueness of solutions to a fractional-order SIQR epidemic model, alongside its intricate chaotic and complex dynamics as functions of the fractional order. The well-posedness of the model solutions,...
One of the great challenges in complex and chaotic dynamics is to reveal the details of its underlying determinism. This can be manifest in the form of temporal correlations or structured patterns in the dynamics of a measurable variable. These tempo...
Through chaos theory, experimental data of hourly time series are analyzed. These time series consist of Radon concentration levels and meteorological variables of temperature, pressure, and relative humidity within the boundary layer and very close...
Analysis of daily solar irradiation variability and predictability in space and time is important for energy resources planning, development, and management. The natural intermittency of solar irradiation is mainly triggered by atmospheric turbulent...
This study explores the application of complex network theory to examine the temporal dynamics of groundwater levels in a region. It presents the first ever application of a coupled chaos theory–complex network framework to investigate the temp...
This work analyzes the behavior of the boundary layer subjected to stresses by obstacles using hourly measurements, in the form of time series, of meteorological variables (temperature (T), relative humidity (RH), and magnitude of the wind speed (WS)...
In this paper, novel variants for the Ensemble Particle Swarm Optimizer (EPSO) are proposed where ten chaos maps are merged to enhance the EPSO’s performance by adaptively tuning its main parameters. The proposed Chaotic Ensemble Particle Swarm Optim...
This paper presents a modification of an image encryption algorithm combining chaos and the Fibonacci matrix by integrating artificial intelligence via a Generative Pre-Trained Transformer (GPT). The goal is to improve the robustness of the algorithm...
Self-organizing systems arise in complex biomechanical structures, human locomotion, and neural control hierarchies, yet quantitative methods for describing order formation and loss of stability remain limited. This study develops a mathematical fram...
Assessing teaching behavior is essential for improving instructional quality, particularly in Physical Education, where classroom interactions are fast-paced and complex. Traditional evaluation methods such as questionnaires, expert observations, and...
This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate...
Discrete neuron models efficiently reproduce complex firing behaviors, while meminductive coupling introduces history-dependent regulation without substantially increasing model complexity. A discrete meminductor is coupled to the Rulkov neuron to co...
Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental science over several decades. Time series of water and matter fluxes and nutrient concentrations from these systems exhi...
22 February 2023
A qualitative study of thermal transfers is carried out from a record of measurements (time series) of meteorological variables (temperature, relative humidity and magnitude of wind speeds) and pollutants (PM10, PM2.5 and CO) in six localities locate...
This paper constructs a continuous dual-channel closed-loop supply chain (DCLSC) model with delayed decision under government intervention. The existence conditions of the local stability of the equilibrium point are discussed. We analyze the influen...
In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of paramet...
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