arXiv subjects

Hammed Olawale Fatoyinbo

Publications and source records attributed to Hammed Olawale Fatoyinbo.

11 recordsLinked to original sources

arXiv2026

Collective Phase Reorganization and Cluster Synchronization in Networks of Coupled Gumowski--Mira Maps

We investigate the collective dynamics of networks composed of diffusively coupled Gumowski-Mira maps and analyze how modifications in the intrinsic dynamics of the local oscillator reorganize the emergent phase structure of the network. The coupling strength and the local control parameter are treated as bifurcation parameters, and the resulting collective states are quantified using the largest Lyapunov exponent, a synchronization error measure, cluster-count statistics, and collective phase-classification diagrams. Two representative regimes of the local dynamics are examined. In the first regime, the network exhibits a smooth and highly organized collective parameter space, featuring a synchronization wedge embedded within an extended region of periodic cluster states. In the second regime, the same coupling architecture yields a fragmented phase organization, comprising disconnected synchronization islands, incoherent domains, and enhanced chaotic-cluster states. These results indicate that variations in the intrinsic dynamics of the individual Gumowski-Mira oscillator do not simply shift synchronization thresholds but can fundamentally restructure the topology of the collective phase space. Our findings thus establish a direct relationship between local nonlinear dynamics and the emergent organization of collective phases in coupled discrete-time networks.

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arXiv2026

Spatiotemporal dynamics and ecological risk factors of highly pathogenic avian influenza A(H5N1) in Canadian wildlife: A One Health surveillance analysis

Highly pathogenic avian influenza A(H5N1) has expanded geographically and ecologically, affecting wild birds, mammalian wildlife, domestic animals, and humans. Wildlife surveillance provides critical early warning for One Health preparedness, yet national-scale analyses integrating host ecology, spatial patterns, seasonality, viral lineage, and risk factors remain limited. This study analysed Canadian wildlife HPAI A(H5N1) surveillance records from 2022 to 2026 to characterise spatiotemporal dynamics and identify factors associated with detection counts. A retrospective analysis of 2,657 detections across 13 provinces and territories was conducted using descriptive epidemiology, spatial clustering methods, and Negative Binomial mixed models. Detections were predominantly avian, with waterfowl and raptors as the major host groups, while mammals accounted for a smaller but epidemiologically important proportion. Detection burden was highest in 2022, with increased activity in autumn and spring. Ontario, Alberta, and British Columbia were identified as major hotspots, with evidence of local clustering in parts of the Prairie region. Reassortant Eurasian-North American lineages dominated detections and were strongly associated with higher detection counts. Modelling results identified year, season, and lineage as key predictors. These findings support risk-based One Health surveillance prioritising high-burden regions, migration-associated periods, key avian host groups, reassortant viral lineages, and continued monitoring of mammalian wildlife.

q-bio.PE↗

arXiv2025

Stochastic Modelling and Analysis of Within-Farm Highly Pathogenic Avian Influenza Dynamics in Dairy Cattle

Highly pathogenic avian influenza (HPAI) has expanded its host range with recent detections in dairy cattle, raising critical concerns regarding within-herd persistence and cross-species spillover. This study develops a stochastic $SEI_sI_aR-B$ compartmental model to analyse HPAI transmission, explicitly accounting for environmental pathogen reservoirs and noise intensities through Wiener processes. The positivity and boundedness of solutions are established, and the disease-free and endemic equilibria are analytically derived. The basic reproduction number is determined using the next-generation matrix method. Numerical simulations confirm that the model dynamics are consistent with theoretical analysis and illustrate how stochastic fluctuations significantly influence disease persistence. Furthermore, sensitivity analysis using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC) identifies the transmission rate from asymptomatic infectious cattle ($β_a$) as the primary driver of transmission. The model effectively captures the dynamics of environmental variability affecting HPAI spread, suggesting that effective control strategies must prioritise the early detection and isolation of asymptomatic carriers alongside environmental management.

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arXiv2025

Fractional order induced bifurcations in Caputo-type denatured Morris-Lecar neurons

We set up a system of Caputo-type fractional differential equations for a reduced-order model known as the {\em denatured} Morris-Lecar (dML) neurons. This neuron model has a structural similarity to a FitzHugh-Nagumo type system. We explore both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies. The main purpose of this study is to report various oscillatory phenomena (tonic spiking, mixed-mode oscillation) and bifurcations (saddle-node and Hopf) that arise with variation of the order of the fractional operator and the magnitude of the coupling strength for the coupled system. Various closed-form solutions as functions of the system parameters are established that act as the necessary and sufficient conditions for the stability of the equilibrium point. The theoretical analysis are supported by rigorous numerical simulations.

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arXiv2024

Dynamical properties of a small heterogeneous chain network of neurons in discrete time

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

nlin.AO↗

arXiv2022

A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters

The border-collision normal form is a canonical form for two-dimensional, continuous maps comprised of two affine pieces. In this paper we provide a guide to the dynamics of this family of maps in the non-invertible case where the two pieces fold onto the same half-plane. We identify parameter regimes for the occurrence of key bifurcation structures, such as period-incrementing, period-adding, and robust chaos. We then apply the results to a classic model of a boost converter for adjusting the voltage of direct current. It is known that for one combination of circuit parameters the model exhibits a border-collision bifurcation that mimics supercritical period-doubling and is non-invertible due to the switching mechanism of the converter. We find that over a wide range of parameter values, even though the dynamics created in border-collision bifurcations is in general extremely diverse, the bifurcation in the boost converter can only mimic period-doubling, although it can be subcritical.

nlin.CD↗

arXiv2022

Dynamical effects of electromagnetic flux on Chialvo neuron map: nodal and network behaviors

We consider the dynamical effects of electromagnetic flux on the discrete Chialvo neuron. It is shown that the model can exhibit rich dynamical behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves, various routes to chaos, fingered chaotic attractors. The system enters chaos via period-doubling cascades, reverse period-doubling route, antimonotonicity, via closed invariant curve to chaos. The results were confirmed using the techniques of bifurcation diagrams, Lyapunov exponent diagram, phase portraits, basins of attraction and numerical continuation of bifurcations. Different global bifurcations are also shown to exist via numerical continuation. After understanding a single neuron model, a network of Chialvo neuron is explored. A ring-star network of Chialvo neuron is considered and different dynamical regimes such as synchronous, asynchronous, chimera states are revealed. Different continuous and piecewise continuous wavy patterns were also found during the simulations for negative coupling strengths.

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arXiv2022

On the analysis of a time varying noise-modulated heterogeneous coupled network of Chialvo neurons under the influence of electromagnetic flux

We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology that not only vary in space but also in time. The variation in time is understood by two coupling probabilities, one for the central-peripheral connections and the other for the peripheral-peripheral connections respectively, that updates the network topology with each iteration in time. We have further reported the rich spatiotemporal patterns like two-cluster states, chimera states, traveling waves, coherent, and asynchronized states that arise throughout the network dynamics. We have also investigated the appearance of a special kind of asynchronization behavior called "solitary nodes" that have wide range of applications pertaining to real-world nervous systems. In order to characterize the behavior of the nodes under the influence of these heterogeneities, we have studied two different metrics called the "cross-correlation coefficient" and the "synchronization error". Additionally, to capture the statistical property of the network, for example, how complex the system behaves, we have also studied a measure called "sample entropy". Various two-dimensional color-coded plots are presented in the study to exhibit how these metrics/measures behave with the variation of parameters. Finally, how the nodes synchronize or asynchronize is shown via one-dimensional bifurcation diagrams of the last instance of the main dynamical variable, i.e., the state variable associated with the membrane potential, against different network parameters.

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arXiv2022

Dynamical Model of Mild Atherosclerosis: Applied Mathematical Aspects

Atherosclerosis is a chronic inflammatory disease occurs due to plaque accumulation in the inner artery wall. In atherosclerotic plaque formation monocytes and macrophages play a significant role in controlling the disease dynamics. In the present article, the entire biochemical process of atherosclerotic plaque formation is presented in terms of an autonomous system of nonlinear ordinary differential equations involving concentrations of oxidized low-density lipoprotein (LDL), monocytes, macrophages, and foam cells as the key dependent variables. To observe the capacity of monocytes and macrophages the model has been reduced to a two-dimensional temporal model using quasi steady state approximation theory. Linear stability analysis of the two-dimensional ordinary differential equations (ODEs) model has revealed the stability of the equilibrium points in the system. We have considered both one- and two- parameter bifurcation analysis with respect to parameters associated to the rate at which macrophages phagocytose oxidised LDL and the rate at which LDL enters into the intima. The bifurcation diagrams reveal the oscillating nature of the curves representing concentration of monocytes and macrophages with respect to significant model parameters. We are able to find the threshold values at which the plaque accumulation accelerates in an uncontrollable way. Further to observe the impact of diffusion, a spatiotemporal model has been developed. Numerical investigation of the partial differential equations (PDEs) model reveals the existence of travelling wave in the system which ensures the fact that the development of atherosclerotic plaque formation follows reaction-diffusion wave.

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arXiv2022

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of dynamical behaviour of the original denatured Morris-Lecar model on parameters is addressed through numerical bifurcation analysis. This allows us to explore the changes in dynamics of the model qualitatively as parameters are varied. Then we investigate the effects of external periodic current and electromagnetic flux on the dynamical properties of the improved denatured Morris-Lecar neuron model. Different types of dynamical behaviour, ranging from regular periodic spiking to complex bursting, are found when the multiple parameters are varied simultaneously. The improved model could be applied to research where simple models are required for physiological and pathophysiological responses in neurons.

math.DS↗

arXiv2021

Influence of Sodium Inward Current on Dynamical Behaviour of Modified Morris-Lecar Model

This paper presents a modified Morris-Lecar model by incorporating the sodium inward current. The dynamical behaviour of the model in response to key parameters is investigated. The model exhibits various excitability properties as the values of parameters are varied. We have examined the effects of changes in maximum ion conductances and external current on the dynamics of the membrane potential. A detailed numerical bifurcation analysis is conducted. The bifurcation structures obtained in this study are not present in existing bifurcation studies of original Morris-Lecar model. The results in this study provides the interpretation of electrical activity in excitable cells and a platform for further study.

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