Rasmikanta Pati

This study investigates the dynamics of a discrete‐time competition model involving two species with nonmonotonic growth rates. The system is formulated through coupled Ricker‐type equations that incorporate both intraspecific and interspecific interactions. This part of the work deals with two fundamental properties: boundedness of the solutions and permanence of the system, which hold provided the parameters are chosen within suitable regimes. All equilibria are examined carefully for their local stability. For the interior equilibrium, explicit conditions are derived for the occurrence of flip and Neimark–Sacker bifurcations. Numerical simulations reveal a rich variety of dynamical behaviors, including stable period‐two cycles, quasiperiodic oscillations, and chaotic dynamics arising through the period‐doubling route, which are further verified by the corresponding maximum Lyapunov exponent (MLE) spectra. Unlike previous studies that mainly investigate isolated dynamical properties, the present work integrates rigorous persistence analysis, explicit bifurcation theory, global parameter‐space exploration, period‐two solution analysis, and numerical evidence of chaos within a unified framework, thereby providing a more comprehensive understanding of two‐species Ricker competition dynamics with nonmonotonic growth.

This study investigates a discrete-time predator–prey model incorporating Allee effects in both species. The prey follows logistic growth with a prey-specific Allee threshold, while the predator grows through prey consumption but suffers its own Allee effect at low densities. The model is formulated as a nonlinear system of difference equations, capturing key ecological interactions and intra-species constraints. A detailed mathematical analysis explores the local stability of equilibria and the emergence of flip and Neimark–Sacker bifurcations, leading to periodic and quasi-periodic dynamics. Special cases with vanishing Allee constants reveal critical impacts on species persistence and extinction. Numerical simulations support the analytical results and illustrate diverse regimes, from stability to complex fractal trajectories. Furthermore, a chaos control strategy based on bifurcation analysis is proposed to stabilize the system dynamics near desired states. The findings highlight the intricate interplay between predation and dual Allee effects in shaping long-term ecological outcomes. In addition, our analysis is supported by several foundational works on nonlinear dynamics, bifurcation theory, and discrete-time predator–prey modeling, which provide important theoretical tools for understanding complex ecological systems [ Gakkhar & Singh , 2012 ; Jing & Yang , 2006 ; Kuznetsov , 1997 ; Liu & Xiao , 2007 ; MacDonald , 2008 ; Wan , 1978 ; Wiggins , 2003 ; Rocha & Taha , 2023 ; Singh et al. , 2019 ; Hassan & Goldar , 2023 ; Goldar , 2025 ; Goldar et al. , 2025b ].

We address the issue regarding big data of high dimensional computation. Various statistical and signal processing techniques are used for compression and dimension reduction in last decade for data mining research. Most prominent technique in recent trend of computation for feature extraction is PCA,ICA, MDS, LDA, DWT, DFT and S-transform. These techniques are being used in different dimension of research arena. In this paper we have tried to dissect wavelet transform in speech processing, image processing with respect to time and frequency domain. After noise free decomposition the observation or samples correlation and similarity computation performed to form cluster. The cluster analysis is based on k-means cluster.