The differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is… (More)
we present a two-dimensional continuous time dynamical system modeling a predator-prey food chain, and based on's modified version of the Leslie-Gower scheme and on the Holling-type II scheme. The main result i$ given in terms of boundedness of solutions, existence of an attracting set and global stability of the coexisting interior equilibrium.
The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear… (More)
We consider a FitzHugh-Nagumo Reaction-Diffusion type system (FHN). The dynamics of the reaction part induces a unique repulsive stationnary point (0, 0) and a unique attractive limit cycle. After a description of the asymptotic behaviour of the FHN system, we deal with the synchronization and control analysis of N coupled FHN systems.
Dynamical behavior of a new piecewise-linear continuous-time three-dimensional autonomous chaotic system is studied. System equilibria and their stabilities are discussed. Routes to chaos and bifurcations of the system are demonstrated with various numerical examples, where the chaotic features are justified numerically via computing the system fractal… (More)
Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. In complex networks, because of the difficulty of formulating the replicator dynamics, most of the previous studies are confined to a numerical level. In this paper, we introduce a vectorial formulation to derive three classes of individuals'… (More)
Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. Previous studies proposed a strategy updating mechanism, which successfully demonstrated that the scale-free network can provide a framework for the emergence of cooperation. Instead, individuals in random graphs and small-world networks do… (More)
Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before… (More)
The aim of this paper is to contribute to the modeling and analysis of complex systems, taking into account the nature of complexity at different stages of the system life-cycle: from its genesis to its evolution. Therefore, some structural aspects of the complexity dynamics are highlighted, leading (i) to implement the morphogenesis of emergent complex… (More)