ENOBONG JOSHUA | University of Uyo , Uyo , Nigeria (original) (raw)

Papers by ENOBONG JOSHUA

J. Math. Comput. Sci., Jun 29, 2021

Modern Applied Science, 2018

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthu... more This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Journal of Mathematics Research, 2016

Journal of Mathematical and Computational Science, 2021

In this study, we examine the Magneto-hydrodynamics (MHD) heat and mass flow of nano-fluid over a... more In this study, we examine the Magneto-hydrodynamics (MHD) heat and mass flow of nano-fluid over a non-linearly permeable stretching sheet. The resulting partial differential equations are converted to a system of ordinary differential equations using the similarity transformation and solved numerically using shooting technique with fourth order Runge-Kutta method. The effect of some fluid parameters on the momentum, thermal and nanoparticle volume fraction boundary layers were expatiated for prescribed surface temperature and constant surface temperature through graphs. An excellent agreement was found when the results obtained in this study were compared with results in previous literature.

Mathematical theory and modeling, 2016

This paper investigates persistence and global dynamics of a tritrophic food chain model consisti... more This paper investigates persistence and global dynamics of a tritrophic food chain model consisting of prey, predator, and super-predator. We establish dissipativeness, ultimate boundedness of an invariant region in the state space of this model via the notion of omega-limit sets, absorbing region and global attractor. We explore Freedman-Waltman theorem, and Bendixson-Dulac theorem to guarantee persistence conditions of the model. Lyapunov’s functionals and Lyapunov-LaSalle invariance principle ensure the existence of global asymptotic stability of the system. Numerical responses, phase-portrait and phase-flows were used to illustrate propositions and lemmas. Key words: Global asymptotic stability; Lyapunov functional; Persistence.

Drug release rate and diffusion are paramount in the delivery of drugs to site of need, whether t... more Drug release rate and diffusion are paramount in the delivery of drugs to site of need, whether the drug administration isenteral or parenteral. These phenomena affect the drug absorption. It has been established that the rate of absorption also plays an important role in the drug release process. Although many of the mathematical models take into account the perfect sink condition, in a real system this assumption may not be true as there are many physiological parameters which may affect the drug delivery process. This study establishes that the desirable situation for drug effectiveness and efficacy is when the drug release rate is small compared to the diffusion rate.

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthu... more This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptot-ically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values. Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Journal of mathematical analysis and applications, 2004

In this paper we consider the existence and uniqueness of positive periodic solution for the peri... more In this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation y′(t)=−a(t)y(t)+λh(t)f(y(t−τ(t))). By the eigenvalue problems of completely continuous operators and theory of α-concave or −α-convex operators and its eigenvalue, we ...

Modern Applied Science

This paper investigates stable proper nodes, stable spiral sinks and stable ω−limit cycles of Ext... more This paper investigates stable proper nodes, stable spiral sinks and stable ω−limit cycles of Extended Rosenzweig-MacAthur Model, which incorporates ratio-dependent functional response on predation mechanism. The ultimate bound-edness condition has been used to predict extinction, co-existence, and exponential convergence scenarios of the model. The Poincare-Bendixson results guarantee existence of periodic cycles of the models. The system degenerate from stable spiral sinks to stable ω−limit cycles as control parameter varies. Numerical simulations are provided to support the va-lidity of theoretical findings.

Journal of Nonlinear Sciences and Applications

A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostk... more A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostkian constructs to explain, and predict cognitive processes during collaborative learning. Learning is re-conceptualized as continuous perturbations of cognitive state which unfolds stable cognitive trajectories near Piagetian equilibrium. The model explicates topologically equivalent cognitive patterns, attributed to multi-modal representation of sensory information presented to the learners. Synchronization of the cognitive model is obtained via active control functions which predicts convergence of cognitive states. The synchronized cognitive model is stabilized using Lyapunov matrix equation. These qualitative behaviors emerged due to learner-to-learner and instructor-to-learner scaffolding driven by cognitive executive functions. The dynamical behaviors of the cognitive model are simulated using control parameters with estimated datasets showing viable cognitive trajectories.

In this paper, we formulated a new topologically equivalence dynamics of an Extended Rosenzweig-M... more In this paper, we formulated a new topologically equivalence dynamics of an Extended Rosenzweig-MacArthur Model. Also, we investigated the local stability criteria, and determine the existence of co-dimension-1 Hopf-bifurcation limit cycles as the bifurcation-parameter changes. We discussed the dynamical complexities of this model using numerical responses, solution curves and phase-space diagrams.

Modern Applied Science, 2011

We examine two-dimensional laminar flow of a liquid with circular hydraulic jump using boundary l... more We examine two-dimensional laminar flow of a liquid with circular hydraulic jump using boundary layer approach, but with the inclusion of a velocity profile approximated by a quadratic function. Our motivation is due to an earlier work of Watson (1964) on radial spread of a liquid over a horizontal plate. We obtain a new relation for the displacement thickness, momentum thickness and position of the jump. Our approximate values based on Pohlhausen (1921) are compared with the exact values due to . The comparison shows the error of about 9% in the shear rate relation on the plate and the error of about 3.5% in the thickness ratio. Our values agree to a large extent with the exact values and also show improvement of our work upon that of with respect to the thickness ratio.

Computer and Information Science, 2013

J. Math. Comput. Sci., Jun 29, 2021

Modern Applied Science, 2018

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthu... more This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Journal of Mathematics Research, 2016

Journal of Mathematical and Computational Science, 2021

In this study, we examine the Magneto-hydrodynamics (MHD) heat and mass flow of nano-fluid over a... more In this study, we examine the Magneto-hydrodynamics (MHD) heat and mass flow of nano-fluid over a non-linearly permeable stretching sheet. The resulting partial differential equations are converted to a system of ordinary differential equations using the similarity transformation and solved numerically using shooting technique with fourth order Runge-Kutta method. The effect of some fluid parameters on the momentum, thermal and nanoparticle volume fraction boundary layers were expatiated for prescribed surface temperature and constant surface temperature through graphs. An excellent agreement was found when the results obtained in this study were compared with results in previous literature.

Mathematical theory and modeling, 2016

This paper investigates persistence and global dynamics of a tritrophic food chain model consisti... more This paper investigates persistence and global dynamics of a tritrophic food chain model consisting of prey, predator, and super-predator. We establish dissipativeness, ultimate boundedness of an invariant region in the state space of this model via the notion of omega-limit sets, absorbing region and global attractor. We explore Freedman-Waltman theorem, and Bendixson-Dulac theorem to guarantee persistence conditions of the model. Lyapunov’s functionals and Lyapunov-LaSalle invariance principle ensure the existence of global asymptotic stability of the system. Numerical responses, phase-portrait and phase-flows were used to illustrate propositions and lemmas. Key words: Global asymptotic stability; Lyapunov functional; Persistence.

Drug release rate and diffusion are paramount in the delivery of drugs to site of need, whether t... more Drug release rate and diffusion are paramount in the delivery of drugs to site of need, whether the drug administration isenteral or parenteral. These phenomena affect the drug absorption. It has been established that the rate of absorption also plays an important role in the drug release process. Although many of the mathematical models take into account the perfect sink condition, in a real system this assumption may not be true as there are many physiological parameters which may affect the drug delivery process. This study establishes that the desirable situation for drug effectiveness and efficacy is when the drug release rate is small compared to the diffusion rate.

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthu... more This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptot-ically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values. Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

Journal of mathematical analysis and applications, 2004

In this paper we consider the existence and uniqueness of positive periodic solution for the peri... more In this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation y′(t)=−a(t)y(t)+λh(t)f(y(t−τ(t))). By the eigenvalue problems of completely continuous operators and theory of α-concave or −α-convex operators and its eigenvalue, we ...

Modern Applied Science

This paper investigates stable proper nodes, stable spiral sinks and stable ω−limit cycles of Ext... more This paper investigates stable proper nodes, stable spiral sinks and stable ω−limit cycles of Extended Rosenzweig-MacAthur Model, which incorporates ratio-dependent functional response on predation mechanism. The ultimate bound-edness condition has been used to predict extinction, co-existence, and exponential convergence scenarios of the model. The Poincare-Bendixson results guarantee existence of periodic cycles of the models. The system degenerate from stable spiral sinks to stable ω−limit cycles as control parameter varies. Numerical simulations are provided to support the va-lidity of theoretical findings.

Journal of Nonlinear Sciences and Applications

A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostk... more A computational cognitive model is derived from nonlinear interactions of (Neo) Piagetian-Vygostkian constructs to explain, and predict cognitive processes during collaborative learning. Learning is re-conceptualized as continuous perturbations of cognitive state which unfolds stable cognitive trajectories near Piagetian equilibrium. The model explicates topologically equivalent cognitive patterns, attributed to multi-modal representation of sensory information presented to the learners. Synchronization of the cognitive model is obtained via active control functions which predicts convergence of cognitive states. The synchronized cognitive model is stabilized using Lyapunov matrix equation. These qualitative behaviors emerged due to learner-to-learner and instructor-to-learner scaffolding driven by cognitive executive functions. The dynamical behaviors of the cognitive model are simulated using control parameters with estimated datasets showing viable cognitive trajectories.

In this paper, we formulated a new topologically equivalence dynamics of an Extended Rosenzweig-M... more In this paper, we formulated a new topologically equivalence dynamics of an Extended Rosenzweig-MacArthur Model. Also, we investigated the local stability criteria, and determine the existence of co-dimension-1 Hopf-bifurcation limit cycles as the bifurcation-parameter changes. We discussed the dynamical complexities of this model using numerical responses, solution curves and phase-space diagrams.

Modern Applied Science, 2011

We examine two-dimensional laminar flow of a liquid with circular hydraulic jump using boundary l... more We examine two-dimensional laminar flow of a liquid with circular hydraulic jump using boundary layer approach, but with the inclusion of a velocity profile approximated by a quadratic function. Our motivation is due to an earlier work of Watson (1964) on radial spread of a liquid over a horizontal plate. We obtain a new relation for the displacement thickness, momentum thickness and position of the jump. Our approximate values based on Pohlhausen (1921) are compared with the exact values due to . The comparison shows the error of about 9% in the shear rate relation on the plate and the error of about 3.5% in the thickness ratio. Our values agree to a large extent with the exact values and also show improvement of our work upon that of with respect to the thickness ratio.

Computer and Information Science, 2013