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The stability of predator–prey interactions in ecosystems is influenced by both inherent species interactions and external factors. For instance, the presence of additional food, as an external factor, may affect the system. To further explore this, a stage-structured predator–prey model is constructed, incorporating the influences of fear and delay on prey-population growth, which provides additional food for immature predators and facilitates cooperative behavior between mature and immature predators. The analysis evaluates the positivity, boundedness, equilibrium points, local stability around each equilibrium point, and certain bifurcations of the system. Additionally, numerical simulations are provided to correspond with the results of the theoretical analysis. It is observed that an appropriate level of fear contributes positively to system stability. While cooperation among predators can benefit immature predators, it also has the potential to harm the overall system. The introduction of additional food complicates the system dynamics, although it benefits predators, it places prey at a disadvantage. Furthermore, we observe a correlation between the level of fear and the effects of additional food, as well as the capacity of additional food to mitigate the influence of delay. [ABSTRACT FROM AUTHOR]

In regular dynamics, discrete maps are model presentations of discrete dynamical systems, and they may approximate continuous dynamical systems. Maps are used to investigate general properties of dynamical systems and to model various natural and socioeconomic systems. They are also used in engineering. Many natural and almost all socioeconomic systems possess memory which, in many cases, is power-law-like memory. Generalized fractional maps, in which memory is not exactly the power-law memory but the asymptotically power-law-like memory, are used to model and investigate general properties of these systems. In this paper we extend the definition of the notion of generalized fractional maps of arbitrary positive orders that previously was defined only for maps which, in the case of integer orders, converge to area/volume-preserving maps. Fractional generalizations of Hénon and Lozi maps belong to the newly defined class of generalized fractional maps. We derive the equations which define periodic points in generalized fractional maps. We consider applications of our results to the fractional and fractional difference Hénon and Lozi maps. [ABSTRACT FROM AUTHOR]

In Bénard-Rayleigh convection we consider the pattern defect in orthogonal domain walls connecting a set of convective rolls with another set of rolls orthogonal to the first set. This is understood as an heteroclinic orbit of a reversible system where the x - coordinate plays the role of time. This appears as a perturbation of the heteroclinic orbit proved to exist in a reduced 6-dimensional system studied by a variational method in Buffoni et al. (J Diff Equ, 2023, https://doi.org/10.1016/j.jde.2023.01.026), and analytically in Iooss (Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection. Preprint, 2023). We then prove for a given amplitude ε 2 , and an imposed symmetry in coordinate y, the existence of a one-parameter family of heteroclinic connections between orthogonal sets of rolls, with wave numbers (different in general) which are linked with an adapted shift of rolls parallel to the wall. [ABSTRACT FROM AUTHOR]

The paper devotes to the synthesis of local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors. The discrete model gives rise to a two-dimensional non-invertible map, whose basins of attraction have complicated topological structures due to the intrinsic multi-stability. The influences of joint parameters on the local dynamics are presented in great details. Both theoretical and numerical results are plotted on the two-dimensional parametric planes. To show more detailed bifurcation structure, the isoclines are extended to higher periodic orbits for detecting the cusps of resonant entrainments. Invariant manifolds and critical curves are employed to illustrate the global dynamics of the model vividly. The tangency and intersections of invariant manifolds expound the process of erosions of basins of attraction. The global bifurcations of basins of attraction are deduced dynamically by critical curves. [ABSTRACT FROM AUTHOR]

Besides consultants and practitioners, some contributions in the organizational economics literature have advocated substituting internal firms’ bureaucracies with markets to regulate internal transactions. However, usually the effects of competition on performance are considered in terms of competition across firms or industries. By contrast, other contributions point out that competition is pervasive inside firms as well. In this paper, we assume that conflict is directly related to the level of competition and propose a model which analyze the dynamics of performance when the manager decides the level of competition observing the group performance. We study the stability of the equilibria and analyze the bifurcations. We show that the fixed point with null performance is a Milnor attractor, and this may suggests why any attempt to move from this unsatisfactory outcome is unsuccessful. [ABSTRACT FROM AUTHOR]

One of the most important problems in the theory of dynamical systems (mentioned in the Palis-Pugh list) is the construction of a stable arc between structural stable diffeomorphisms in the space of diffeomorphisms. The paper considers the gradient-like diffeomorphisms of 2-torus that induce an isomorphism of fundamental groups determined by a matrix ( − 1 0 0 − 1 ). We prove that all such diffeomorphisms are stable isotopy connected. [ABSTRACT FROM AUTHOR]

Identification of bifurcation diagrams in nonlinear systems is of great importance for resilient design and stability analysis of dynamical systems. Data-driven identification of bifurcation diagrams has a significant advantage for large dimensional systems where analysis of the equations is not possible, and for experimental systems where accurate system equations are not available. In this work, a novel forecasting approach to predict bifurcation diagrams in nonlinear systems is presented using system trajectories before instabilities occur. Unlike previous techniques, the proposed method considers a varying bifurcation parameter during the system response to perturbations. Combined with an asymptotic analysis provided by the method of multiple scales eliminates the requirement of using multiple measurements and allows the novel technique to predict the bifurcation diagram using a single system recovery. The proposed approach allows stability analyses of nonlinear systems with limited access to experimental or surrogate data. The novel technique is demonstrated through its application to a Hopf bifurcation, highlighting its inherent advantages. Subsequently, the method is employed in the analysis of an aeroelastic system that shows both supercritical and subcritical Hopf bifurcations. The findings reveal great accuracy, achieved with a reduced number of measurements, while enhancing versatility. • Novel forecasting technique predicts bifurcation diagrams using single system recovery. • Method uses system trajectories before instabilities with varying bifurcation parameters. • Combines data-driven forecasting and method of multiple scales asymptotic analysis. • Demonstrated accuracy and versatility with both supercritical and subcritical Hopf bifurcations in aeroelastic systems. [ABSTRACT FROM AUTHOR]