This paper discusses on the dynamics and bifurcations of a two-dimensional discrete prey-predator model with Bazykin functional response and linear harvesting in predator. Compared to Bazykin prey-predator model which focuses on competition for other resources, Bazykin functional response include predator competition for prey and predator saturation. Limited studies on Bazykin functional response especially in discrete model highlight the novelty of this research. A semi-discretisation method is applied to derive the model from continuous to discrete. The stability at each fixed point is summarised by applying related lemma and definition. The occurrences of Neimark-Sacker and flip bifurcations are established through the Centre Manifold Theorem and supported by numerical simulations. The coexistence fixed point first loses stability through Neimark-Sacker bifurcation before becoming stable over an intermediate parameter range. Then, the fixed point undergoes flip bifurcation giving rise to periodic and chaotic dynamics. Simulations by MATLAB and MATCONTM are included by providing the bifurcation, phase portrait and time series diagrams. The discrete model displays interesting dynamical behaviours such as transition of Neimark–Sacker to flip bifurcation, quasiperiodic oscillations, periodic solutions and chaos brought on by harvesting. This paper highlights that intensive harvesting leads to chaotic behaviour of prey population and subsequently lead to predator extinction. The results signifies that intensive harvesting combined with predator competition can drastically alter the system dynamics, offering crucial ecological insights into sustainable harvesting strategies.
Sericulture is an important socioeconomic sector in many developing countries; however, environmental temperature changes and Nuclear Polyhedrosis Virus (NPV) epidemics significantly limit its output. A new nonlinear five compartmental mathematical model that integrates silkworm population dynamics, NPV transmission, environmental viral persistence, piezoelectric energy generation and temperature regulation is developed and analyzed in this work. Newtonian heat exchange controlled by piezoelectric-assisted thermal control, temperature-dependent viral transmission and mortality, Holling type II saturation in environmental virus accumulation and the logistic growth of healthy silkworms are all included in the model. Extensive analytical studies establish the existence and uniqueness of solutions, positivity and boundedness. Eigenvalue criteria and Jacobian analysis are used to determine local stability conditions and identify virus-free and endemic equilibrium points. The virus-free equilibrium is shown to be globally asymptotically stable under threshold conditions defined by fundamental reproduction number using a Lyapunov function. The main determinants of system behavior, according to sensitivity analysis, are infection rate, virus decay rate and temperature dependent mortality. According to numerical simulations, maintaining favorable thermal condition is associated with reduced NPV proliferation and improved silkworm survival, while suboptimal temperatures are associated with increased viral amplification and higher larval mortality. By using piezoelectric energy harvesting, rearing temperature may potentially be regulated, outbreak intensity may decrease and healthy silkworm persistence may improve under modeled conditions. In addition, three-dimensional phase trajectories illustrate the interdependent feedback between environmental regulatory mechanisms, viral load and host activity. The proposed framework connects epidemiological dynamics with temperature regulation based on renewable energy, may provide a theoretical basis for future studies on temperature-regulated and energy-assisted sericulture systems. This study presents a unified modeling approach that may support the development of more stable silk production systems in line with global sustainability goals by combining mathematical ecology, virology, and green energy technology.
The exact mathematical form of the empirical Pareto Principle is derived using the optimum power law which is based on information theory. It is shown that the 80–20 Rule is approximately 70–20 for populations below 400, which means that 20
In this article, we study a nonlinear neuron membrane model describing the propagation of action potentials along nerve fibers, incorporating nonlinear elastic effects and higher–order dispersion. By applying the Hirota bilinear transformation, the given equation is converted into an equivalent bilinear form, which provides a suitable analytical framework for systematic construction of exact solutions. To enrich the functional solution space, we introduce a bilinear neural network method (BNNM), where neural network architectures are used as structured symbolic generators rather than numerical approximators. Both single-hidden-layer and double-hidden-layer configurations are constructed to generate exact analytical solutions. Through symbolic coefficient matching assisted by Maple, multiple admissible parameter sets are obtained. The presented framework yields a diverse family of exact wave structures, involving lump solutions, breather-type oscillatory waves, soliton–lump interaction states, double-period lump superpositions, three-wave interaction patterns, and hybrid lump–rogue wave excitations. The derived solutions are expressed in compact Hirota form and signified via three-dimensional, density, and contour visualizations, revealing strong spatial localization, temporal modulation, nonlinear energy redistribution, and coherent phase-locked propagation. The results represent that the neural-bilinear approach offers a powerful and systematic mechanism for constructing rich nonlinear wave families in neuron-type models. These analytical structures contribute to understanding localized pulse transmission, multi-wave interaction dynamics, and transient amplification phenomena in excitable biological media.
This study develops a fractional-order (FO) reaction–diffusion (RD) model to capture the spatiotemporal adoption dynamics of Remote Healthcare Services (RHS) in geographically constrained regions. The model integrates sociological mechanisms social contagion, external influence, relapse, and spatial diffusion within a framework enhanced by Caputo fractional derivatives to account for memory effects and historical dependencies in adoption behavior. A numerical scheme based on Grunwald–Letnikov (GL) discretization in time and finite differences method (FDM) in space is implemented and analyzed for stability using the von Neumann method adapted to FO systems. Simulation results demonstrate the emergence of spatially heterogeneous adoption patterns, damped responses to perturbations, and the influence of memory on long-term dynamics. The present work focuses on the mathematical formulation, numerical discretization, and stability analysis of the FO-RD model. Empirical calibration using field data from the Chittagong Hill Tracts (a region characterized by natural barriers and limited infrastructure) and scenario-based policy evaluations are identified as essential next steps but lie outside the scope of this paper. The model provides a robust predictive tool for evaluating policy interventions, optimizing resource allocation, and supporting equitable healthcare deployment in remote and underserved areas.
We investigate and partially explain some of the ≪ counterintuitive ≫ effects that arise in a probabilistic analogue of Conway’s ≪ life ≫ cellular automaton when cells are allowed to come to life or die out with certain probabilities depending on the number of living neighbors. Some biological analogies turned out to be appropriate. One of the most intriguing observations: if we add to the standard ≪ B3S23 ≫ rules of the ≪ Game of Life ≫ cellular automaton a stochastic rule whereby a dead cell is born with five neighbors with probability p, then for 0< p < 0.09 this leads to an increase in population compared to the standard rules, while for p > 0.1 it leads to degradation.
Although trade-offs are ubiquitous in living nature, they often remain concealed from researchers. Here I describe an opposite possibility: a trade-off may be apparent as a negative across-population correlation between beneficial traits, but not actually present. I describe two simple and mutually non-exclusive mechanisms by which such "ghost trade-offs" can emerge: (a) elimination of the least fit ("double-weak") genotypes, while the moderately fit ("single-weak") trait combinations survive, and (b) evolutionary suicide, i.e., extinction of the most fit ("double-fit") lineages. Such "ghost trade-offs" may be common in nature and should be recognized and distinguished from real trade-offs.
In this manuscript, Heimburg’s model, a mathematical framework for understanding the propagation of electromechanical pulses in biomembranes and nerves is studied. The model interprets the lipid bilayer of the cell membrane to be a substance that undergoes phase transitions. It signifies that the membrane has a nonlinear behavior to electrical perturbations. Through Lie symmetry analysis, the fundamental symmetries of the governing equation are exposed. In addition, Ibragimov’s general conservation theorem is used to generate additional conservation laws, ensuring the solutions’ physical applicability. Leveraging the recently developed extended direct algebraic technique (EDAM) and Riccati–Bernoulli sub-ODE method, we explore the dynamics of electromechanical pulses in nerves. Numerous soliton solution types are extracted, such as periodic-singular, peakon, bright, dark, kink, combo, and mixed-type solitons. The Hamiltonian characteristic is used to further analyze the stability of these diverse solutions and validate the system’s conserved energy features. Furthermore, by utilizing the linear stability approach to study the modulational instability (MI) of a chosen model, offering insights into the circumstances in which perturbations decrease or increase. The resulting two-dimensional, three-dimensional, and contour visualizations of the electromechanical pulse provide valuable insights into nerve functionality, with potential applications in the biological sciences.
The sciences divide into those that discover laws and those that reconstruct histories. We argue that this division does not reflect a difference in subject matter, but a difference in epistemic regime. Law-based sciences operate under episodic closure: systems are idealized so that the outcomes of prior interactions do not alter the rules governing future ones. This regime-defining idealization (distinguished from pragmatic idealization) underlies the predictive successes of physics, but creates a systematic blind spot for evolutionary dynamics. We formalize this distinction using Stability-Driven Assembly (SDA), a minimal non-equilibrium framework in which differential persistence couples episodes into population-level evolutionary dynamics without genes, replication, or predefined fitness functions. Representing compositional objects as λ -calculus terms, we show that episodic science studies isolated λ -reductions under fixed rules, while evolutionary science studies populations of λ -instantiations whose outputs re-enter the space of operators. The resulting dynamics are self-modifying and irreducibly sequential: each step rewrites the conditions for the next. A four-quadrant taxonomy locates episodic science, evolutionary science, and two commonly conflated intermediate cases: formal possibility and constructive potential, within a single framework. From this analysis we derive the “No Free Telos” constraint: in constructive systems where population feedback reshapes the effective dynamics at each step, the cost of predicting future states cannot in general be reduced below the cost of simulating the generative history. The resulting framework bridges episodic and historical sciences, not by reducing one to the other, but by identifying population-level memory as the structural condition that transforms law-governed episodes into open-ended evolutionary processes.
Understanding how conscious cognition remains stable under uncertainty, conflict, and perturbation requires a framework that links neural dynamics to the geometry of evolving representational states. Here we develop Recursive Informational Curvature (RIC), a neurogeometric framework in which conscious access is modeled as a stability regime of trajectories on a stratified informational manifold. In this framework, recursive gain, symbolic entropy dispersion, and loop-level timing coherence jointly determine whether neural activity remains within closure-supporting regimes or approaches collapse. We formalize this balance through an effective curvature index, 𝒦(t) , defined relative to a declared critical boundary 𝒦_crit , and through circulation-based timing statistics that quantify phase-organized loop stability. The theory integrates three coupled geometric layers: a Fisher layer for precision-weighted discriminability, a Finsler layer for direction-dependent transition cost, and a Hermitian layer for phase-coded recursive coordination. We further propose mechanistic hypotheses linking identifiable cortical neuronal classes, including mirror circuits, von Economo neuron-rich salience territories, TPJ mentalizing ensembles, and prefrontal phase-modulating hubs, to class-specific curvature control. To connect the framework to data, we specify measurement-facing estimators for gain, symbolic entropy structure, loop instability, and effective curvature, and we provide a reduced EEG-based empirical analysis showing that a geometry-sensitive neural state-space proxy is related to moral judgment bias, while broader socially mediated outcomes are not captured by this reduced measure alone. RIC therefore offers a formal and operational framework for studying stability, collapse, and recovery in conscious dynamics across theoretical, empirical, and translational settings.
In this paper we introduce a model to estimate weight gain of farm animals in depends on several parameters. We introduce an analytical approach for analysis of the introduce model with account of changing of the above parameters in space and time, as well as taking into account the nonlinearity of the considered process. We consider the possibility to accelerate and decelerate of the fattening of farm animals.
Cancer incidence is influenced by a combination of extrinsic and genetic factors. We hypothesized that cancers with similar incidence patterns may suggest shared etiologies. Age-standardized incidence rates for 36 cancer types across 185 countries were obtained from GLOBOCAN 2022. Pairwise Spearman’s correlation coefficients were computed, and network clustering analyses were performed using six community detection algorithms: Leiden, Surprise, Walktrap, Girvan-Newman, Infomap, and spectral clustering. A dominant cluster was consistently identified, comprising kidney, pancreatic, colorectal, and thyroid cancers, as well as hematological malignancies. The second cluster comprised lung cancer, mesothelioma, melanoma, and non-melanoma skin cancer, which were grouped with head and neck cancers in some algorithms. Kaposi’s sarcoma, nasopharyngeal cancer, and salivary gland cancer were classified individually. The dominant cluster showed significantly greater enrichment of shared mutational signatures (cosine similarity, p = 0.041) and recurrent mutation overlap (Jaccard similarity, p = 0.025) than expected by chance. Additionally, eigenvector centrality positively correlated with global cancer incidence rates. Overall, this unsupervised network analysis of global cancer epidemiology identifies biologically coherent clusters that reflect potentially shared etiological mechanisms and may inform public health intervention strategies.
The classification of plant varieties is a key task in plant breeding and variety registration. Red fescue (Festuca rubra L.), a widely cultivated grass species, includes numerous closely related varieties, making automated classification a challenging multi-class problem. This study aimed to develop and evaluate a multilayer perceptron (MLP) neural network combined with a subset-based decision framework for accurate classification of red fescue varieties and recognition of previously unseen varieties. The study analyzed 76 varieties described by seven morphological features. To address the complexity of the multi-class problem, the dataset was divided into multiple subsets and the effectiveness of different partitioning strategies was evaluated. A confidence-based and majority-based decision rule (majority ratio ≥ 0.9 and mean Softmax confidence ≥ 0.8) was introduced to improve the reliability of final predictions and enable open set recognition. The model was evaluated using accuracy, precision, F1 score, and recall. The most optimal solution was to divide the dataset into 15 subsets, with the first subset containing six varieties and the remaining subsets containing five varieties each. This approach provided the best balance between predictive performance and decision consistency, enabling correct classification of known varieties and stable detection of unknown samples. Combining MLP neural networks with strategic subset division and confidence-driven decision rules offers a robust solution to high-dimensional, multi-class classification challenges in plant variety recognition. The model’s ability to recognize new varieties is crucial for its practical application, ensuring the algorithm’s flexibility. This is particularly useful in agriculture and horticulture, where new varieties are bred over the years.
The complexity and diversity inherent in living organisms have long been regarded as significant challenges to the formulation of a universally accepted definition of life. Life is manifested across diverse forms, characterized by properties such as growth, reproduction, responsiveness, adaptation, and homeostasis. However, these traits are not exclusively confined to living systems; they have also been observed, to varying extents, in certain non-living entities. As a result, the conceptual boundary between the living and the non-living has been rendered increasingly ambiguous. In this study, the transformation of non-living matter into living systems is investigated, and it is demonstrated that this process lacks a precise temporal threshold that clearly marks the emergence of life. Through mathematical analysis, it is shown that no comprehensive definition of life captures a distinct separation within the chemical continuum that leads from inanimate to animate matter. The absence of uniquely defining features that unequivocally distinguish living organisms from non-living entities is thereby revealed. This analysis challenges traditional assumptions regarding the definability of life, emphasizing the need for a revised conceptual framework that accounts for the continuum between non-living and living systems.
The gene has remained a central organizing concept in biology for more than a century, yet its definition has become increasingly difficult to reconcile with contemporary molecular and genomic evidence. This article combines a historical review with a conceptual perspective to examine the evolution of the gene concept from Mendelian heredity to postgenomic biology. Early gene concepts assumed discreteness and stable relationships between genes and traits. These assumptions were highly productive but became inadequate as gene regulation, RNA processing, epigenetic modification, and long-range genomic interactions were discovered. Rather than converging on a refined definition, biological research progressively expanded the range of phenomena that gene concepts were required to accommodate. By synthesizing key developments across classical genetics, molecular biology, and genomics, this review explains why defining the gene has become empirically challenging while the gene itself remains indispensable in biological practice. On this basis, a pragmatic working definition of the gene is proposed that is grounded in DNA sequence and reproducible transcriptional output under regulatory control, while remaining compatible with contemporary genomic research.
This study employs a three-tier food chain framework to examine the influence of the Allee effect on prey foraging efficiency and physiological stability. The model incorporates a Holling type II functional response between the prey and mesopredator, while the top predator is a sexually reproducing species that interacts with the mesopredator through a Crowley-Martin formulation. The system’s sensitivity to variations in the half-saturation constant is analyzed to investigate bifurcation phenomena and the onset of chaos. Chaotic behavior is characterized quantitatively using the largest Lyapunov exponent, revealing that changes in the half-saturation constant strongly affect the system’s dynamical complexity. To account for spatial processes, the model is extended into a diffusive framework, and the resulting reaction-diffusion system is analyzed for Turing instabilities. Analytical conditions for diffusion-driven instability are derived, and the emergence of spatial patterns is confirmed through numerical simulations. The findings indicate that mutual interference among predators can both destabilize and stabilize the system, depending on parameter values. Increased top predator interference tends to promote stability, whereas enhanced residual decline in predator normalization leads to instability.
The human gastrointestinal system is colonized by microbiota, consisting of more than 100 trillion cells, which is essential for gastrointestinal development, nutrient absorption, and immune system function. Disruption of the microbiota has been linked to obesity, metabolic syndromes, inflammatory bowel disorders, and cancer. The microbiota has also been linked to nervous system development, and animal studies have suggested that the gut microbiota influences behavior of the host, with significant effects on host fitness. We hypothesize that at least some of these effects on host behavior, in part mediated by factors produced by the microbiota, have adaptive value for the microorganisms. There is evolutionary evidence of host-symbiont co-evolution; the microbiota may have evolved mechanisms to alter host behavior to enhance the fitness of the microbial species living within the host. In this sense, host behavior is an extended phenotype of its microbiota. Therefore, human behavior can also be interpreted as being an extended phenotype of the microbiota, which is a fundamental conclusion of this work. Analyzing the evolutionary tradeoffs with respect to the microbiota and its relationship with the host can inform optimized approaches to enhance host fitness. Such approaches can take advantage of the fitness “needs” of the microbiota as a tool to improve host health and well-being, thus decreasing human morbidity and mortality. We discuss methods for testing this hypothesis and consider its implications.
This article characterizes Oyama's concept of ontogenesis of information formally. I apply the mathematical notion of synergistic information to the framework proposed by Griffiths et al. (2015) for developmental information and specificity. This allows us to examine the specificity revealed by the interaction of variables as a result of interventions on interactions. I define Developmental Synergistic Information as the specificity of interacting variables obtained by measuring how much mutual information interventions on interactions carry about the effect variable. To formalise this concept, I use partial information decomposition, one of the most robust frameworks for analysing synergistic information. Some examples of developmental synergistic information are presented. Finally, I consider the philosophical implications of developmental synergistic information, arguing that it supports important tenets of organism-centered biology: (i) synergistic information has ontogeny-order is generated in epigenesis; (ii) such information is non-transmissible through channels of inheritance-the specificity of outcomes must be reconstructed anew in each generation; (iii) the developmental organism (or any synergistic system under consideration) is itself a cause of development-causation resides in the coaction of developmental variables; and (iv) the developmental context of information must be taken into account-that developmental causation is always embedded in and constrained by a developmental matrix of other specifiers.
Biological systems under chronic resource overload often exhibit asymmetric transitions into high-load states that are difficult to reverse. Within a bow-tie (hourglass) framework, such dynamics arise when diverse inputs are funnelled through a constrained regulatory core governing system-level responses. Here, lake eutrophication and human obesity are analysed as structurally distinct yet dynamically analogous manifestations of resource overload. In lakes, external nutrient inputs and internal biogeochemical feedbacks drive shifts from clear-water, macrophyte-dominated regimes to hypertrophic, phytoplankton-dominated states. In humans, sustained caloric surplus interacts with metabolic–hormonal regulation and behavioural–social drivers to promote the development and stabilisation of obesity. In both systems, reinforcing feedbacks organise around a central regulatory core, reducing flexibility, generating hysteresis, and constraining recovery trajectories. Despite these similarities, key asymmetries emerge. In lakes, dynamics under overload are dominated by a limited set of reinforcing feedbacks, whereas in obesity regulation remains distributed across interacting physiological, behavioural, and environmental domains. In both cases, responses involve cascade-like propagation of effects, taking the form of trophic cascades in lakes and cross-domain feedback cascades in humans. These results show that similar system-level dynamics, including alternative stable states, tipping points, and hysteresis with constrained reversibility, can arise from differently structured regulatory architectures. The comparison demonstrates that reversibility is system-specific and shaped by the organisation of the regulatory core and associated feedbacks. Interpreting eutrophication and obesity through a bow-tie framework provides a comparative, architecture-based perspective on resource overload and helps explain why effective interventions require coordinated actions targeting multiple components of the feedback structure.
