Modeling and analysis of a coupled SIS bi-virus model

This article focuses on properties of equilibria and their associated regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincaré–Hopf theorem is used to derive a general result providing a sufficient condition for the system to have a unique equilibrium. The condition involves the Jacobian of the system at possible equilibria and ensures that the system is in fact locally exponentially stable. We apply this result to the susceptible–infected–susceptible (SIS) networked epidemic model, and a generalized Lotka–Volterra system. We use the result further to extend the SIS model via the introduction of decentralized feedback controllers, which significantly change the system dynamics, rendering existing Lyapunov-based approaches invalid. Using the Poincaré–Hopf approach, we identify a necessary and sufficient condition, under which the controlled SIS system has a unique nonzero equilibrium (a diseased steady state), and monotone systems theory is used to show that this nonzero equilibrium is attractive for all nonzero initial conditions. A counterpart condition for the existence of a unique equilibrium for a nonlinear discrete-time dynamical system is also presented.

Tabu search (TS) is a metaheuristic that guides a local heuristic search procedure to explore the solution space beyond local optimality. It has achieved widespread successes in solving practical optimization problems. This paper proposes the stochastic TS strategy for discrete optimization and makes an investigation of its global convergence. The strategy considered introduces the Metropolis criterion and simulated annealing process into a general framework of TS. It has been proved that the strategy converges asymptotically to global optimal solutions, and satisfies the necessary and sufficient conditions for global asymptotic convergence. Furthermore, it produces a higher convergent rate than the simulated annealing algorithm.

Evolutionarily stable strategies and short-term selection in Mendelian populations re-visited

Simulated annealing (SA) is a generic optimization method that is quite popular because of its ease of implementation and its global convergence properties. However, SA is widely reported to converge very slowly, and it is common practice to allow extra freedom in its design at the expense of losing global convergence guarantees. A natural way to increase the flexibility of SA is to allow the objective function and the communication mechanism to be temperature-dependent, the idea being to gradually reveal the complexity of the optimization problem and to increase the mixing rate at low temperatures. We call this general class of annealing processes stochastic continuation (SC). In the first part of this paper, we introduce SC starting from SA, and we derive simple sufficient conditions for the global convergence of SC. Our main result is interesting in two respects: first, the conditions for global convergence are surprisingly weak--in particular, they do not involve the variations of the objective function with temperature--and second, exponential cooling makes it possible to be arbitrarily close to the best possible convergence speed exponent of SA. The second part is devoted to the application of SC to the problem of producing aesthetically pleasing drawings of undirected graphs. We consider the objective function defined by Kamada and Kawai (Inf Process Lett 31(1):7---15, 1989), which measures the quality of a drawing as a weighted sum of squared differences between Euclidean and graph-theoretic inter-vertex distances. Our experiments show that SC outperforms SA with optimal communication setting both in terms of minimizing the objective function and in terms of standard aesthetic criteria.

In the first part of our theses we give sufficient conditions for the absolute convergence of the double Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to double Fourier series. In the second part we give sufficient conditions for the absolute convergence of the double Walsh-Fourier series of a function. These sufficient conditions are formulated in terms of (either global or local) dyadic moduli of continuity and s-bounded fluctuation.

We prove a new convergence condition for the activity expansion of correlation functions in equilibrium statistical mechanics with possibly negative pair potentials. For non-negative pair potentials, the criterion is an if and only if condition. The condition is formulated with a sign-flipped Kirkwood–Salsburg operator and known conditions such as Kotecký–Preiss and Fernández–Procacci are easily recovered. In addition, we deduce new sufficient convergence conditions for hard-core systems in mathbb {R}^d and mathbb {Z}^d as well as for abstract polymer systems. The latter improves on the Fernández–Procacci criterion.

Profit rates equalization and balanced growth in a multi-sector model of classical competition

Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses

An SIRS model is developed to account for precautionary measures and immunity loss. The existence and stability of equilibria are studied. It is shown that precautionary measures can induce Hopf bifurcations leading to the occurrence of cyclical behavior. The model is then extended to a two-patch scenario to explore how disease spread patterns are influenced by dispersal (travel). Theoretical analyses establish the stability of the disease-free equilibrium, the basic reproduction number, and thresholds related to travel rates. The persistence of the system, as well as the existence of boundary and endemic equilibria, are also discussed. Using Hopf bifurcation theory, we further examine the interaction between nonlinear incidence functions, travel rates, and precaution delay effects in shaping the stability of the endemic equilibrium. The findings reveal a strong connection between reduced infection rates due to precaution and the emergence of Hopf bifurcations, emphasizing the importance of timely and accurate disease information in curbing the spread of diseases. Additionally, the study highlights the significant impact of different infection force functions on equilibrium stability, underscoring the critical role of precautionary measures in disease transmission mechanisms. The results also show the diverse effects of travel rates on disease spread, suggesting that restricting travel may not always lead to favorable outcomes. This underscores the necessity for governments to consider multiple factors comprehensively in their efforts to prevent and control diseases.

Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks

We propose a stage-structured model of childhood infectious disease transmission dynamics, with the population demographics dynamics governed by a certain family and population planning strategy giving rise to nonlinear feedback delayed effects on the reproduction ageing and rate. We first describe the long-term aging-profile of the population by describing the pattern and stability of equilibrium of the demographic model. We also investigate the disease transmission dynamics, using the epidemic model when the population reaches the positive equilibrium (limiting equation). We establish conditions for the existence, uniqueness and global stability of the disease endemic equilibrium. We then prove the global stability of the endemic equilibrium for the original epidemic model with varying population demographics. The global stability of the endemic equilibrium allows us to examine the effects of reproduction ageing and rate, under different family planning strategies, on the childhood infectious disease transmission dynamics. We also examine demographic distribution, diseases reproductive number, infant disease rate and age distribution of disease, and as such, the work can be potentially used to inform targeted age group for optimal vaccine booster programs.

Average-consensus filter problem is investigated for a mixed-order multi-agent system, which consists of first-order and second-order agents, and the proportional-integral consensus filter algorithms are proposed for the agents with different constant inputs. Based on generalized Nyquist stability criterion, sufficient convergence conditions are obtained for the multiagent system under a fixed, symmetric and connected topology to achieve the asymptotic consensus seeking of average value of agents' constant inputs. Besides, the delay-dependent convergence conditions are obtained for the multi-agent systems with identical communication delay. Numerical simulations are presented to illustrate the correctness of our results.

In this paper, we consider continuous-time semidecentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.

This contribution discusses the global convergence behavior of iterative algorithms solving nonlinear approximation problems via a sequence of linear approximation problems. Essentially there are two sufficient conditions for global convergence: 1) The algorithm should have only critical points as accumulation points. 2) The parametrization should imply that the parameters of refined approximations have accumulation points. For some important nonlinear families of approximating functions it is proved that the above conditions hold, provided that the parametrization is restricted to suitable subfamilies.

This correspondence first shows that the global convergence analysis of the method proposed in the above paper is incomplete. Then we provide a counter example to show that the sufficient condition for global convergence is incorrect