Modelling has become an eminent tool in the study of ecological systems. Ecological modelling can help implement sustainable development, mathematical models, and system analysis that explain how ecological processes can promote the sustainable management of resources. In this paper, we also chose a four‐dimensional discrete‐time Lotka–Volterra ecological model and analyzed its dynamic behavior. In particular, we derived the parametric conditions for the existence of biologically feasible solutions and the stability of the fixed points. We also provided graphs to study the spectrum behavior of all fixed points. In addition, we have seen that when the intrinsic dynamics of the population exceed a certain threshold, the system bifurcates. This particular range of inherent population dynamics depends on the values of other biological parameters and the initial population. We proved that the instability of the model resulted in Neimark–Sacker and period‐doubling bifurcations. To confirm these two types of bifurcation, we used bifurcation theory, and to find the direction of bifurcation, we used graphical results. Mainly, through novel periodic plots, we confirm the coexistence of the population and the possible equilibrium states. We apply Marotto’s theorem to verify the existence of chaos in the system. To control the chaos, we use a hybrid control feedback methodology. Finally, we provide numerical examples to illustrate our theoretical results. The outcomes of the numerical simulations show chaotic long‐term behavior across an extensive range of parameters.

We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension‐one and codimension‐two bifurcation analysis, and chaos control in a predator‐prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension‐two 1 : 2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results.

Network analysis involves using graph theory to understand networks. This knowledge is valuable across various disciplines like marketing, management, epidemiology, homeland security, and psychology. An essential task within network analysis is deciphering the structure of complex networks including technological, informational, biological, and social networks. Understanding this structure is crucial for comprehending network performance and organization, shedding light on their underlying structure and potential functions. Community structure detection aims to identify clusters of nodes with high internal link density and low external link density. While there has been extensive research on community structure detection in single‐layer networks, the development of methods for detecting community structure in multilayer networks is still in its nascent stages. In this paper, a new method, namely, IGA‐MCD, has been proposed to tackle the problem of community structure detection in multiplex networks. IGA‐MCD consists of two general phases: flattening and community structure detection. In the flattening phase, the input multiplex network is converted to a weighted monoplex network. In the community structure detection phase, the community structure of the resulting weighted monoplex network is determined using the Improved Genetic Algorithm (IGA). The main aspects that differentiate IGA from other algorithms presented in the literature are as follows: (a) instead of randomly generating the initial population, it is smartly generated using the concept of diffusion. This makes the algorithm converge faster. (b) A dedicated local search is employed at the end of each cycle of the algorithm. This causes the algorithm to come up with better new solutions around the currently found solutions. (c) In the algorithm process, chaotic numbers are used instead of random numbers. This ensures that the diversity of the population is preserved, and the algorithm does not get stuck in the local optimum. Experiments on the various benchmark networks indicate that IGA‐MCD outperforms state‐of‐the‐art algorithms.