We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map f can have in a neighborhood of one of its ...fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of f at this point. Our approach is inspired on similar Poincaré type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.
Interdependent networks can practically model several complex systems. In such networks, particularly critical infrastructure networks, cascading failure is the most common phenomenon observed, and ...hence, has gradually become a prevalent research topic in recent years. We combine statistical methods to build a cascading failure propagation model based on discrete dynamical systems. Based on a discrete-time model, a failure pattern is proposed wherein the units in a system continuously fail due to cascading events or malevolent attacks. Then, we analyze the model in combination with practical scenarios.
•Risk propagation model of cascading failure based on discrete Dynamical Systems.•Conditional failure probability makes proposed model universal to practical world.•Capable of coupling multi-layer networks.•Discrete dynamic system transfers the cascade relationship on the time scale.•Propose a continuous failure pattern to simulate continuous failure events.
Lawvere's open problem on quotient toposes has been solved for boolean Grothendieck toposes but not for non-boolean toposes. As a simple and non-trivial example of a non-boolean topos, this paper ...provides a complete classification of the quotient toposes of the topos of discrete dynamical systems, which, in this context, are sets equipped with an endofunction. This paper also offers an order-theoretic framework to address the open problem, particularly useful for locally connected toposes.
Our result is deeply related to monoid epimorphisms. At the end of this paper, utilizing the theory of lax epimorphisms in the 2-category Cat, we explain how (non-surjective) monoid epimorphisms from N correspond to (non-periodic) behaviors in discrete dynamical systems.
This paper examines a discrete predator–prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator ...species. Furthermore, juvenile hunting along with its negative effects in the form of prey counterattack is considered. This paper provides a comprehensive analysis of the existence and stability conditions pertaining to all possible fixed points of this system. The impact of the parameters reflecting prey growth and prey refuge is thoroughly discussed. This paper delves into the occurrence of the Neimark–Sacker bifurcation and period-doubling bifurcation, specifically in relation to the parameters associated with prey growth rate and prey refuge. Numerous numerical simulations are presented in order to validate the theoretical findings.
In this paper we study the long-term behavior of the p-adic dynamical systems associated with the Sigmoid Beverton-Holt model that arises in population dynamics. The corresponding fixed points, ...maximal Siegel disks, attractors, and periodic trajectories are analyzed in the projective line P1(Qp). Moreover, the Julia and Fatou sets associated with these dynamical systems are also examined.
Suppose that a closed surface S⊆R3 is an attractor, not necessarily global, for a discrete dynamical system. Assuming that its set of wild points W is totally disconnected, we prove that (up to an ...ambient homeomorphism) it has to be contained in a straight line. As a corollary we show that there exist uncountably many different 2-spheres in R3 none of which can be realized as an attractor for a homeomorphism.
Our techniques hinge on a quantity r(K) that can be defined for any compact set K⊆R3 and is related to “how wildly” it sits in R3. We establish the topological results that (i) r(W)≤r(S) and (ii) any totally disconnected set having a finite r must be contained in a straight line (up to an ambient homeomorphism). The main result follows from these and the fact that attractors have a finite r.
•Dynamic oligopolistic models to describe heterogenous banks that compete in the loan market.•Adaptive behavior in a context of limited information and bounded computational ability, and in the ...presence of non-performing loans.•Policy insights on how different risk factors interact to generate banking stress and fragility.•Evolutionary interpretation of the Nash equilibrium, Adaptive Best Reply, Gradient Dynamics.•Monetary policies set by the Central Bank produce a variety of lending behaviors, affecting banking stability.
This paper proposes dynamic oligopolistic models to describe heterogenous banks that compete in the loan market. Two boundedly rational banks adopt an adaptive behavior to increase their profits under different assumptions of limited information and bounded computational ability, in the presence of a share of credits that might not be reimbursed (i.e. non-performing loans). Each Nash equilibrium is an equilibrium point of the dynamic adjustments as well. Thus, the repeated strategic interactions between banks may converge to a rational equilibrium according to the parameters’ values and the initial conditions.
As a case study, we assume an isoelastic nonlinear demand and linear costs as in Puu (1991), and we analyze the influence of the economic parameters on the local stability of the unique equilibrium, as well as the kinds of attractors that characterize the long-run behavior of the banks. Moreover, we study the global structure of the basins of attraction and the degrees of stability of the Nash equilibrium under two different dynamic adjustments: adaptive best reply and gradient dynamics. We obtain interesting policy insights on how different risk factors interact to generate banking stress and fragility. Finally, we show that different monetary policies set by the Central Bank may produce a variety of lending behaviors affecting banking stability.
The purpose of this paper is to present a way to associate “relevant” reductions to subgroupoids G of X×Z×X with G(0) finite. In order to obtain such a reduction we use singular value decomposition ...of a matrix associated with the groupoid .
•We provide a discrete-time fractional-order SEIR measles epidemic model with vaccination.•The existence of steady states and the asymptotic stability of the steady states are discussed.•The ...occurrence of flip bifurcation, Neimark-Sacker bifurcation and codim 2 flip-Neimark-Sacker bifurcation are captured using an algebraic criterion method.•Theoretical results are validated numerically.
In this paper, a discrete-time SEIR measles epidemic model with fractional-order and constant vaccination is investigated. The basic reproduction number with an algebraic criterion are used to study the local asymptotic stability of the equilibrium points. Two types of codimension one bifurcation namely, flip and Neimark-Sacker (N-S) bifurcations and their intersection codimension two flip-N-S bifurcation, are discussed. The necessary and sufficient conditions for detecting these types of bifurcation are derived using algebraic criterion methods. The criterions employed are based on the coefficients of characteristic equations rather than the properties of eigenvalues of Jacobian matrix. The output is a semi-algebraic system composed of a set of equations, inequalities and inequations. These criterions represent appropriate conditions for codim-1 and codim-2 bifurcations of high dimensional maps.
•We propose a cellular automata approach to texture recognition.•Transition function based on local binary features.•Chaotic evolution controlled by a weighting parameter.•The method is evaluated on ...the classification of benchmark textures.•State-of-the-art methods are outperformed in terms of classification accuracy.
Texture recognition is one of the most important tasks in computer vision and, despite the recent success of learning-based approaches, there is still need for model-based solutions. This is especially the case when the amount of data available for training is not sufficiently large, a common situation in several applied areas, or when computational resources are limited. In this context, here we propose a method for texture descriptors that combines the representation power of complex objects by cellular automata with the known effectiveness of local descriptors in texture analysis. The method formulates a new transition function for the automaton inspired by local binary descriptors. It counterbalances the new state of each cell with the previous state, in this way introducing an idea of “controlled deterministic chaos”. The descriptors are obtained from the distribution of cell states. The proposed descriptors are applied to the classification of texture images both on benchmark data sets and a real-world problem, i.e., that of identifying plant species based on the texture of their leaf surfaces. Our proposal outperforms other classical and state-of-the-art approaches, especially in the real-world problem, thus revealing its potential to be applied in numerous practical tasks involving texture recognition at some stage.
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