An in-depth knowledge of pedagogical approaches can help improve the formulation of effective and efficient pedagogy, tools and technology to support and enhance the teaching and learning of Mathematics in higher institutions. This study investigated students' perceptions of the challenges of blended e-learning tools in the teaching and learning of mathematics. The study is a descriptive survey design conducted with thirty undergraduate students of the University of Uyo, Nigeria. A research questionnaire of students' perceptions on the challenges of blended e-learning tools in mathematics was used to elicit responses. The questionnaire has three sections of the perceived challenges of blended e-learning tools in mathematics; availability, accessibility and students' ICT skills towards utilization of blended e-learning tools. Data were analyzed using SPSS at the 0.05 level of significance. The results revealed non-availability, non-accessibility and inadequate students' ICT skills towards the utilization of blende e-learning tools for the teaching and learning mathematics. The overall results revealed that there is significant difference on students' perceptions towards the challenges of blended e-learning tools. Based on the research findings, the institution and instructors need to identify the perceived challenges and opportunities of blended e-learning and provide practical support such as provision of Virtual Learning Environment (VLE) to diversified students learning of mathematics. The study could be used as proactive response towards the institutions' preparedness on the development of blended e-learning approaches in terms of content design models and pedagogical approach for the teaching and learning of mathematics.

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.

This work was carried out in collaboration between all authors. Author EEJ formulated a dimensionless dynamical system and generated its numerical simulations, author ETA used Brouwer's and coincidence degree algorithm to established existence of solutions. Authors OA and CEM proved the uniqueness of the periodic solution. The final manuscript was completed by author ETA. All authors read and approved the final manuscript.

<p>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.</p>

<p>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.</p>