Hidden Dynamics Research Articles

Navigating psychological barriers in agricultural innovation adoption: A multi-stakeholder perspective

Agricultural innovation is pivotal for enabling cleaner production within the sector. Nonetheless, smallholder farmers in the Global South encounter functional and psychological challenges impeding innovation adoption efforts. Existing literature tends to narrowly focus on common barriers associated with individual innovations, often limiting the broader significance of psychological hindrances. This study takes a unique approach by delving primarily into the realm of psychological barriers, encompassing internal challenges that impede adoption, and explores external support strategies to overcome such hindrances. A multi-stakeholder approach was employed to gather validated insights based on data from eighteen semi-structured interviews involving rice farmers and agricultural technology companies. Research findings revealed that trust, effort, attitudinal, and normative barriers are prominent psychological hindrances to innovation adoption. To this effect, pertinent enabling factors and overcoming strategies should demonstrate clear benefits, infuse trust, reduce effort requirements, and develop human capital. This research is among the first to demystify and categorise psychological barriers and corresponding overcoming strategies into an integrated framework. The resulting framework allows for a novel and comprehensive analysis of the potential strategies to overcome the psychological barriers collectively, a complex issue involving interrelations and hidden dynamics that are challenging to explore otherwise. This study contributes to the Innovation Resistance Theory through its application within the context of smallholder farmers and leads to implications to expedite the transformation towards a more sustainable and innovative agriculture sector.

Design and Analysis of a Novel Fractional-Order System with Hidden Dynamics, Hyperchaotic Behavior and Multi-Scroll Attractors

The design of chaotic systems with complex dynamic behaviors has always been a key aspect of chaos theory in engineering applications. This study introduces a novel fractional-order system characterized by hidden dynamics, hyperchaotic behavior, and multi-scroll attractors. By employing fractional calculus, the system’s order is extended beyond integer values, providing a richer dynamic behavior. The system’s hidden dynamics are revealed through detailed numerical simulations and theoretical analysis, demonstrating complex attractors and bifurcations. The hyperchaotic nature of the system is verified through Lyapunov exponents and phase portraits, showing multiple positive exponents that indicate a higher degree of unpredictability and complexity. Additionally, the system’s multi-scroll attractors are analyzed, showcasing their potential for secure communication and encryption applications. The fractional-order approach enhances the system’s flexibility and adaptability, making it suitable for a wide range of practical uses, including secure data transmission, image encryption, and complex signal processing. Finally, based on the proposed fractional-order system, we designed a simple and efficient medical image encryption scheme and analyzed its security performance. Experimental results validate the theoretical findings, confirming the system’s robustness and effectiveness in generating complex chaotic behaviors.

Shedding light on hidden dynamics: partner controlling behavior and women's alcohol consumption in Ghana

BackgroundWhile existing literature suggests a link between alcohol intake and the perpetuation of controlling behaviors, reverse association is yet to be established. Therefore, our study aims to extend the current understanding of the determinants of alcohol consumption among women in Ghana by investigating the association between partner controlling behavior and women’s past month’s alcohol consumption.MethodsThe study relied on data from the 2022 Ghana demographic and health survey. Analysis was based on observations from 5137 women with complete information on partner controlling behavior and past month alcohol consumption. Descriptive statistics, bivariate and multivariate logistic regression were computed. All analyses were executed in STATA version 18.ResultsAbout 15.05% of women consumed alcohol; 37.31% of the respondents had partners who exhibited controlling behaviors. Women who reported experiencing partner controlling behaviors were 1.19 times more likely to engage in alcohol consumption compared to those who did not report such behaviors (AOR = 1.19; 95% CI 1.01–1.41). Additionally, the study identified other significant predictors of alcohol consumption among women, including experiences of sexual violation (AOR = 1.62; 95% CI 1.21–2.15) and richer wealth (AOR = 0.76; 95% CI 0.59–0.97).ConclusionIn conclusion, experiencing partner controlling behavior is associated with higher risk of alcohol consumption. Thus, underscoring the importance of addressing not only individual-level factors but also relational dynamics in understanding and addressing alcohol intake among women. Policy makers and program implementers must prioritize interventions aimed at promoting healthy relationship dynamics and addressing gender-based power imbalances. Furthermore, healthcare providers should be trained recognize and address partner controlling behaviors and sexual violence as part of comprehensive interventions for reducing alcohol consumption among women.

A New Fractional Discrete Memristive Map with Variable Order and Hidden Dynamics

This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathematical operator, namely, a fractional variable-order Caputo-like difference operator, is employed to establish the fractional form of the map with short memory. The numerical simulation results highlight its excellent dynamical behavior, revealing that the addition of the piecewise fractional order makes the memristive-based Duffing map even more chaotic. It is characterized by distinct features, including the absence of an equilibrium point and the presence of multiple hidden chaotic attractors.

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

Complex dynamics of a sub-quadratic Lorenz-like system

Abstract Motivated by the generic dynamical property of most quadratic Lorenz-type systems that the unstable manifolds of the origin tending to the stable manifold of nontrivial symmetrical equilibria forms a pair of heteroclinic orbits, this technical note reports a new 3D sub-quadratic Lorenz-like system: x ˙ = a ( y − x ) \dot{x}=a(y-x) , y ˙ = c x 3 + d y − x 3 z \dot{y}=c\sqrt[3]{x}+{\rm{d}}y-\sqrt[3]{x}z and z ˙ = − b z + x 3 y \dot{z}=-bz+\sqrt[3]{x}y . Instead, the unstable manifolds of nontrivial symmetrical equilibria tending to the stable manifold of the origin creates a pair of heteroclinic orbits. This drives one to further investigate it and reveal its other hidden dynamics: Hopf bifurcation, invariant algebraic surfaces, ultimate bound sets, globally exponentially attractive sets, existence of homoclinic and heteroclinic orbits, singularly degenerate heteroclinic cycles, and so on. The main contributions of this work are summarized as follows: First, the ultimate boundedness of that system yields the globally exponentially attractive sets of it. Second, the existence of another heteroclinic orbits is also proved by utilizing two different Lyapunov functions. Finally, on the invariant algebraic surface z = 3 4 a x 4 3 z=\frac{3}{4a}\sqrt[3]{{x}^{4}} , the existence of a pair of homoclinic orbits to the origin, and two pairs of heteroclinic orbits to two pairs of nontrivial symmetrical equilibria is also proved by utilizing a Hamiltonian function. In addition, the correctness of the theoretical results is illustrated via numerical examples.

Hidden dynamics and control of a Filippov memristive hybrid neuron model

Hidden dynamics and control of a Filippov memristive hybrid neuron model

Hidden Dynamics, Multistability and Synchronization of a Memristive Hindmarsh–Rose Model

Reliable neuron models play an essential role in identifying the electrical activities, global bifurcation patterns, and dynamic mechanisms of neurons in electromagnetic environments. Considering that memristive autapse can characterize the self-induced effect of neurons, a five-dimensional Hindmarsh–Rose (HR) neuron model involving electric and magnetic fields is established. The detailed existence and stability analyses for equilibrium points are performed, and the complex time-varying stability, saddle-node bifurcation, and Hopf bifurcation behaviors are demonstrated. Interestingly, the bistable structures consisting of quiescent state and periodic bursting modes near the subcritical Hopf bifurcation and counterintuitive dynamic phenomena can be induced via appropriately adjusting the memristive current. Accordingly, the mechanism of positive feedback autaptic current decreases its firing frequency, while negative feedback autaptic current promotes its excitability and is revealed by the fast–slow dynamic analysis. Generally, the system possesses period-adding bifurcation patterns and comb-shaped chaotic structures as demonstrated by the numerical results. Importantly, it can be confirmed that the electrical activities and multistability of the system can be accurately predicted by analyzing the global dynamic behaviors of the Hamilton energy. Furthermore, it is verified that the unidirectional coupling controller involving energy is far more efficient and consumes lower energy than electrical synaptic coupling in achieving complete synchronization with mismatched parameters. These results provide potential guidance and help for further research in computational neuroscience and the design and control of intelligent sensors.

Feature importance measures to dissect the role of sub-basins in shaping the catchment hydrological response: a proof of concept

Understanding the response of a catchment is a crucial problem in hydrology, with a variety of practical and theoretical implications. Dissecting the role of sub-basins is helpful both for advancing current knowledge of physical processes and for improving the implementation of simulation or forecast models. In this context, recent advancements in sensitivity analysis tools could be worthwhile for bringing out hidden dynamics otherwise not easy to distinguish in complex data driven investigations. In the present work seven feature importance measures are described and tested in a specific and simplified proof of concept case study. In practice, simulated runoff time series are generated for a watershed and its inner 15 sub-basins. A machine learning tool is calibrated using the sub-basins time series for forecasting the watershed runoff. Importance measures are applied on such synthetic hydrological scenario with the aim to investigate the role of each sub-basin in shaping the overall catchment response. This proof of concept offers a simplified representation of the complex dynamics of catchment response. The interesting result is that the discharge at the catchment outlet depends mainly on 3 sub-basins that are consistently identified by alternative sensitivity measures. The proposed approach can be extended to real applications, providing useful insights on the role of each sub-basin also analyzing more complex scenarios.

A Framework for Interactive Development of Simulation Models with Strategical–Tactical–Operational Layering Applied to the Logistics of Bulk Commodities

CONTEXT–Simulation modelling provides insight into hidden dynamics underlying business processes. However, an accurate understanding of operations is necessary for fidelity of the model. This is challenging because of the need to extract the tacit nature of operational knowledge and facilitate the representation of complex processes and decision-making patterns that do not depend on classes, objects, and instantiations. Commonly used industrial simulation, such as Arena®, does not natively support the object-oriented constructs available for software development. OBJECTIVE–This paper proposes a method for developing simulation models that allow process-owners and modellers to jointly build a series of evolutionary models that improve conceptual validity of the executable computer model. APPROACH-Software and Systems Engineering principles were adapted to develop a framework that allows a systematic transition from conceptual to executable model, which allows multiple perspectives to be simultaneously considered. The framework was applied to a logistics case study in a bulk commodities distribution context. FINDINGS–The method guided the development of a set of models that served as scaffolds to allow the natural flow of ideas from a natural language domain to Arena® code. In doing so, modeller and process-owners at strategic, tactical, and operational levels developed and validated the simulation model. ORIGINALITY—This work provides a framework for structuring the development of simulation models. The framework allows the use of non-object-oriented constructs, making it applicable to SIMAN-based simulation languages and packages as Arena®.

Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system

Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system

Hidden extreme multistability and its control with selection of a desired attractor in a non-autonomous Hopfield neuron

In this article, a single nonautonomous Hopfield neuron is investigated. This neuron involves a new hyperbolic-type memristor as self-synaptic weight. The current–voltage characteristics of the new memristor enables the observation of the hysteresis loop with more than one pinch. The analysis of the equilibria highlighted that the model has hidden dynamics. A plethora of nonlinear phenomena is obtained during the analysis of the model. Among them, the coexistence of an infinite number of symmetric bifurcation diagrams each having its intrinsic energetic singularity. The zooms of the initial condition diagrams enable to observe the coexistence of ten periodic hidden attractors and nine chaotic hidden attractors. The model also exhibited the antimonotonicity phenomenon characterized by the coexistence of an infinite number of bubbles. The control of up to nine coexisting hidden chaotic attractors in a specific domain of the initial condition is successfully realized. This control is achieved by choosing initially an attractor as a designated survivor using the feedback term method. It is then found that the employed method can also be used to control multistability in a system without an equilibrium point. An analog circuit of the model is also designed in PSpice, to further support the results of the theoretical investigations.

Generating grid chaotic sea from system without equilibrium point

The dynamical system without equilibrium point is considered having hidden dynamics. It is relatively difficult to locate the attractor in the state space as its attraction basin has nothing to do with the equilibrium point. Especially, generation of multi-scroll chaos from no-equilibrium system is a challenging task. In this paper, using sine function, a modified Sprott-A system without equilibrium point but with perpetual points is presented. In particular, this system has the conservative property of zero-sum Lyapunov exponents and thus can generate chaotic sea rather than an attractor. The locations of the scrolls of chaotic sea are found having potential relevance to the sine nonlinearities and perpetual points. Different number of scrolls can be extended only adjusting the system parameters. Three cases of five-term Sprott-A system variants with single-direction multi-scroll/multi-double-scroll chaotic sea and two-direction grid chaotic sea are demonstrated. Besides, hidden tori are found coexisting with the chaotic sea. Numerical simulations and hardware experiments both confirm the complex dynamics of the system.

Expressions of the Interior: Physiognomic Knowledge in Lavater, Goethe, and Alexander von Humboldt

Abstract This article examines the role of Johann Caspar Lavater’s (1741-1801) physiognomic ideas in shaping the relationship between the natural sciences and aesthetics at the turn of the nineteenth century. Using the examples of Johann Wolfgang von Goethe’s early morphological writing and Alexander von Humboldt’s Ideen zu einer Physiognomik der Gewächse (1806), it makes the case for the importance of Lavater’s »scientific« physiognomy for understanding the discursive- epistemological shift from the sensual empiricism of the eighteenth century to the perception of the invisible around 1800. Far from a direct line of intellectual- historical continuity from Lavater to Goethe and Humboldt, this article contends that the diffuse uptake of physiognomic concepts by exponents of Romantic science gave them a new meaning in relation to the study of ›life‹ and its hidden dynamics as well as with respect to the roles of art and aesthetics in comprehending nature’s ›interior‹.

Bifurcation analysis of a class of generalized Hénon maps with hidden dynamics

Although continuous systems such as the Chua circuit are known as systems with hidden attractors, hidden attractors also exist in classical discrete maps, such as a generalized Hénon map. A hidden attractor is an attractor that does not overlap with its own attracting region in its vicinity, which makes it difficult to visualize. In this paper, a local bifurcation analysis method for discrete maps is described, and the bifurcation analysis of the generalized Hénon map is performed using the method. The bifurcation structure, as the parameters are changed, shows a certain law, and the interesting Neimark–Sacker bifurcation and period‐doubling bifurcation are confirmed to occur simultaneously. It was also found that the hidden attractors exist in the rectangular characteristic chaotic regions, and they appear relatively frequently near the window of chaos. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Modeling of memristor-based Hindmarsh-Rose neuron and its dynamical analyses using energy method

It has been extensively studied to employ memristors to model the relationship between the electromagnetic field and the membrane potential, especially for the research of modeling and dynamical analyses of electrical activity using HR neurons with memristors. This paper proposes a novel 4D HR model with a threshold flux-controlled memristor (MHR), which describes the electromagnetic induction effect. The proposed 4D HR model retains the original HR properties and can describe the complex dynamics of neurons' electrical activities with fewer parameters than the existing models. Due to the particularity of the no equilibrium point of the MHR model, the hidden dynamics are found in the proposed MHR model. The generalized Hamiltonian function is fully derived for the MHR neuron model using Helmholtz's theorem. The simplest form of the Hamiltonian form is given by assigning special values. The average Hamiltonian energy and its bifurcation are employed to find the connection between energy and firing patterns. The band-limited white noise is also studied, and it is found that it positively influences the electrical activities in the proposed MHR system.

Small towns (re)growing old. Hidden dynamics of old-age migration in shrinking regions in Germany

ABSTRACT In many regions with long-term structural economic and demographic problems, small towns are shrinking as their urban centres, they are losing population, jobs, vibrancy and infrastructure. Yet, knowledge about their trajectories remains vague as studies on urban shrinkage have so far focused on large cities. When monitoring population change of small towns in Germany, there are ambiguous findings concerning their recent development: On the one hand, natural and migration balances were mostly negative and the population is ageing. On the other, they have become target locations of old-age in-migration. Hidden behind general demographic decline, the towns’ elderly populations are growing in relative and absolute terms. Our paper wants to shed light on these processes. It draws upon explorative empirical research in small towns in Germany. We will present, firstly, elderly’s motivations and actual relocation decisions. Secondly, we will show that these trends remain even largely out of sight of municipal decision makers. By way of conclusion, we argue that urban shrinkage is not a linear but rather a contingent process where overlapping trends, agencies and decisions of various actors together with the more fine-grained unevenness of spatial development can result in unexpected and ambivalent local trajectories.

Spectrally Silent Protein Reaction Dynamics Revealed by Time-Resolved Thermodynamics and Diffusion Techniques.

Biological functions essentially consist of a series of chemical reactions, including intermolecular interactions, and also involve the cooperation of a number of biological molecules performing these reactions. To understand this function at the molecular level, all steps of the reactions must be elucidated. However, since the biosystems including the surrounding environment are notably large, the reactions have to be elucidated from several different approaches. A variety of techniques have been developed to obtain structural information, and the knowledge of the three-dimensional structure of biomolecules has increased dramatically. Contrarily, the current information on reaction dynamics, which is essential for understanding reactions, is still not enough. Although frequently used techniques, such as spectroscopy, have revealed several important processes of reactions, there are various hidden dynamics that are not detected by these methods (silent dynamics). For example, although water molecules are essential for bioreactions, dynamics of the protein-water interaction are very difficult to trace and spectrally silent. Transient association/dissociations of proteins with partner proteins are difficult to observe. Another important property to understand the reaction of proteins is fluctuations, which are random movements that do not change the average structure and energy. The importance of fluctuations has been pointed out in order to explain enzymatic activity; however, it is extremely difficult to detect changes in fluctuation during a reaction. In this Account, unique time-resolved methods, time-resolved thermodynamics, and time-resolved diffusion methods, both of which are able to detect silent dynamics in solution at physiological temperature, are described.Thermodynamic properties are important for characterizing materials, in particular, macromolecules such as biomolecules. Therefore, the data available regarding these properties, for several stable proteins, is abundant. However, it is almost impossible to characterize short-lived intermediate species in irreversible reactions using traditional thermodynamic techniques. Similarly, although the translational diffusion coefficient is a useful property to determine the protein size and intermolecular interactions, there have been no reports revealing reaction dynamics. The transient grating (TG) method enables us to measure these quantities in a time-resolved manner for a variety of irreversible reactions. With this method, it is now possible to study biomolecule reactions from the viewpoint of thermodynamic properties and diffusion, and to elucidate reaction dynamics that cannot be detected by other spectroscopic methods.Here, the principles of the methodologies used, their characteristic advantages, and their applications to protein reactions are described. The TG measurements of octopus rhodopsin revealed a spectrally hidden intermediate and determined an energetic profile along the reaction coordinate. This emphasizes that the measurement in solution, not for trapped intermediates, is important to characterize the reaction intermediates. The application of these methods to a blue light sensor PixD revealed many spectrally silent dynamics as well as the importance of fluctuation for the reaction. As an example of the time-resolved heat capacity change and transient thermal expansion measurements, the reaction of PYP was briefly described. The reaction scheme of another blue light sensor protein, phototropins, and a spectrally silent DNA binding process of EL222 were fully elucidated by the time-resolved diffusion method.

Breaking of integrability and conservation leading to Hamiltonian chaotic system and its energy-based coexistence analysis.

In this paper, a four-dimensional conservative system of Euler equations producing the periodic orbit is constructed and studied. The reason that a conservative system often produces periodic orbit has rarely been studied. By analyzing the Hamiltonian and Casimir functions, three invariants of the conservative system are found. The complete integrability is proved to be the mechanism that the system generates the periodic orbits. The mechanism route from periodic orbit to conservative chaos is found by breaking the conservation of Casimir energy and the integrability through which a chaotic Hamiltonian system is built. The observed chaos is not excited by saddle or center equilibria, so the system has hidden dynamics. It is found that the upgrade in the Hamiltonian energy level violates the order of dynamical behavior and transitions from a low or regular state to a high or an irregular state. From the energy bifurcation associated with different energy levels, rich coexisting orbits are discovered, i.e., the coexistence of chaotic orbits, quasi-periodic orbits, and chaotic quasi-periodic orbits. The coincidence between the two-dimensional diagram of maximum Lyapunov exponents and the bifurcation diagram of Hamiltonian energy is observed. Finally, field programmable gate array implementation, a challenging task for the chaotic Hamiltonian conservative system, is designed to be a Hamiltonian pseudo-random number generator.

Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method

This work investigates the dynamics of the Chua circuit with cubic polynomial nonlinearity using methods for stability analysis based on linearization and frequency response. Root locus technique maps eigenvalues of the linearized system in order to analyze the local stability, which allows to verify dynamic features, motion patterns, and attractor topologies. The method based on describing functions allows analyze effects of the cubic nonlinearity in the system, as well as predict equilibrium and fixed points, periodic and chaotic orbits, limit cycles, multistability and hidden dynamics, unstable states, and bifurcations. The stability of the Chua circuit with cubic polynomial nonlinearity is analyzed using both approaches in order to identify and map dynamics in parameter spaces. Numerical investigations based on computational simulations corroborate the theoretical results obtained using this stability analysis. This theoretical analysis and the numerical investigations present interesting insights about the dynamics of the Chua circuit with cubic polynomial nonlinearity and provides a design tool for electro-electronic implementations.