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Artificial intelligence has become the most widely used and trusted component of research in almost all disciplines of science and technology, starting from engineering, online businesses, and industry, to biotechnology and agriculture. Successful rice crops with maximum yield and weed management are the target set by several developed as well as developing countries, based on a combination of cultural and chemical control methods. In this paper, the weed control strategy through the competition model is documented with the aid of the time-series forecasting tool of artificial intelligence. A time-dependent computational framework is built based on the real data, and by utilizing supervised learning algorithm, incorporated with delay. It is emphasized during this research that the accurate precision of time delays in competition models can help in developing the weed control strategies more efficiently and can further support in implementing these strategies as precision models for other crop protection challenges.

Recently Conery proposed a backward execution algorithm for AND-parallel execution of logic programs, and Ng and Leung extended it. They adopt the same data structure called mark(s) set to store information about failure history during AND-parallel evaluation of clauses. Both of the two algorithms essentially have the same rationale with minor differences and have been considered correct, largely due to their intuitive persuasiveness. We closely re-examine those algorithms and find out that they are incorrect. Their incorrectness comes from oversimplification of failure situations. Our analyses focused on the mark(s)-set-based backtrack literal selection are presented. We also propose another backtrack literal selection method based on the mark(s) set, and prove its correctness.

We present a classical interspecific competition model. Individuals compete for a resource on a common patch and can go to a refuge. It is assumed that if species would remain on the competition patch, species 1 survives and species 2 would go extinct. Therefore, species 1 is Locally Superior Competitor (LSC) and species 2 Locally Inferior Competitor (LIC). We study the effects of density dependent dispersal from the competition patch to the refuge on the global outcome of competition. We study two cases. The first case considers LSC density dependent dispersal of the LIC trying to escape competition and going to its refuge when the LSC density is large. The second case considers aggressiveness of LIC leading to LIC density dependent dispersal of the LSC. We show that under some conditions, tactic 2 can allow the LIC to survive and even provoke global extinction of the LSC.

We study a competition model of two competing species in population biology having exponential and rational growth functions described by Alexander et al. [1992]. They observed that, for some choice of parameters, the competition model has a chaotic attractor $A$ for which the basin of attraction is riddled. Here, we give a detailed analysis to illustrate what happens when the normal parameter in this model changes. In fact, by varying the normal parameter, we discuss how the geometry of the basin of attraction of $A$, the region of coexistence or extinction, changes and illustrate the transitions between the set $A$ being an asymptotically stable attractor (extinction of rational species), a locally riddled basin attractor and a normally repelling chaotic saddle (extinction of exponential species). Additionally, we show that the riddling and the blowout bifurcation occur. Numerical simulations are presented graphically to confirm the validity of our results. In particular, we verify the occurrence of synchronization for some values of parameters. Finally, we apply the uncertainty exponent and the stability index to quantify the degree of riddling basin. Our observation indicates that the stability index is positive for Lebesgue for almost all points whenever the riddling occurs.

The purpose of this paper is to study the effect of cross diffusion in a competition model with stage structure, under homogeneous Neumann boundary condition. It will be shown that cross diffusion cannot only destabilize a uniform positive equilibrium, it can also help diffusion to induce instability of the uniform positive equilibrium. Moreover, stationary patterns can arise from the effect of cross diffusion.

In this paper, almost periodic solution of a n-species Lotka–Volterra competition system with grazing rates and diffusions is investigated. By using the method of upper and lower solutions and Schauder fixed point theorem as well as Lyapunov stability theory, we give sufficient conditions under which the strictly positive space homogeneous almost periodic solution of the system is globally asymptotically stable. Moreover, some numerical simulations are given to validate our theoretical analysis.

Population ecology theory is replete with density-dependent processes. However, trait-mediated or behavioral indirect interactions can both reinforce or oppose density-dependent effects. This paper presents the first two species competitive ODE and PDE systems, where the non-consumptive behavioral fear effect and the Allee effect, a density-dependent process, are both present. The stability of the equilibria is discussed analytically using the qualitative theory of ordinary differential equations. It is found that the Allee effect and the fear effect change the extinction dynamics of the system and the number of positive equilibrium points, but they do not affect the stability of the positive equilibria. We also observe standard co-dimension one bifurcation in the system by varying the Allee or fear parameter. Interestingly, we find that the Allee effect working in conjunction with the fear effect can bring about several dynamical changes to the system with only fear. There are three parametric regimes of interest in the fear parameter. For small and intermediate amounts of fear, the Allee + fear effect opposes dynamics driven by the fear effect. However, for large amounts of fear the Allee + fear effect reinforces the dynamics driven by the fear effect. The analysis of the corresponding spatially explicit model is also presented. To this end, the comparison principle for parabolic PDE is used. The conclusions of this paper have strong implications for conservation biology, biological control as well as the preservation of biodiversity.

In this paper, we report some recent theoretical work of Du-Shi¹⁴ , Du-Liang¹² and Du-Peng-Wang¹³ that examines the effect of environmental changes in three well-known diffusive population models, each modeling the interaction of two population species in a common habitat. For each model, we consider the situation that one of the two species is endangered and a simple protection zone is created in the habitat for the endangered species. The focus is on the effect of the protection zone on the dynamics of the two species systems. We demonstrate that, though the effects of the protection zone on the dynamical behavior of the three systems are significantly different from each other, they all share one important property, namely, there exists a critical patch size for the protection zone: If the protection zone is below this size, each model behaves similarly to the non-protection zone case, but every model undergoes profound changes in dynamical behavior once the protection zone is above the critical patch size, and in such a case the endangered species is always saved from extinction.