Equilibrium point

Colman, AM, & Wilson, JC (1997). Antisocial personality disorder: An evolutionary game theory analysis. Legal and Criminological Psychology, 2, 23-34. [Discussed in R. Matthews, “Game Theory Backs Crackdown on Petty Crime”, New Scientist, 1997, 154(2078), 18; “La ...

In this paper, a new simple 4D smooth autonomous system is proposed, which illustrates two interesting rare phenomena: first, this system can generate a four-wing hyperchaotic and a four-wing chaotic attractor and second, this generation occurs under condition that the system has only one equilibrium point at the origin. The dynamic analysis approach in the paper involves time series, phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps, to investigate some basic dynamical behaviors of the proposed 4D system. The physical existence of the four-wing hyperchaotic attractor is verified by an electronic circuit. Finally, it is shown that the fractional-order form of the system can also generate a chaotic four-wing attractor.

Using ideas from complexity theory and its application in the areas of ecology, biology, chemistry and medicine this paper shows how the paradigm of complexity is able to offer the conceptual frame in which they can project, evaluate and coordinate processes ...

This paper deals with modeling and simulations on a supply/recovery energy system with a DC motor used to propel an electrical vehicle. The system architecture is presented, and the analyze of each system element is done. The mathematical models of the elements are taken in account in order to obtain the overall system model. The simulations prove that the stability system conditions are achieved to ensure the desired system functionality.

In this paper, a new numerical-symbolic Matlab program for the analysis of three-dimensional chaotic systems is introduced. The program provides the users with a GUI (Graphical User Interface) that allows us to analyze any continuous three-dimensional system with a minimal input (the symbolic ordinary differential equations of the system along with some relevant parameters). Such an analysis can be performed

Abstract: The term “stability ” has many different meanings and its interpretation and application in various sciences is not absolutely identical. Historically, stability has been first formally defined in mathematical form by Lyapunov to describe equilibrium behaviour of the solar system. Lyapunov stability considers the behaviour of a system solution if its initial state is in the neighbourhood of an equilibrium point. Conceptually, it states that the equilibrium point is stable if all solutions originating in its neighbourhood forever remain “close enough ” to equilibrium. Due to its precise definition and well-established mathematical technique, Lyapunov stability has found a widespread application outside its original context, particularly to analyse solutions of mathematical models of biological communities in order to determine conditions they must satisfy to be stable. Research of this kind has been a dominating trend and, in words of Justus (2006), set much of the agenda o...

In this paper we will observe the model of competitive types and it will be analyzed using the nullcline method. It will be shown that this model has four points of equilibria, which are stable or unstable depending on the parameters a and b. The local stability of these points was investigated and global dynamics was determined using nullcline methods, that is, the bases of attraction of these points were shown.

This work presents a control strategy for coordination of multiple robots based on artificial vision to measure the relative posture between them, in order to reach and maintain a specified formation. Given a leader robot that moves about an unknown trajectory with unknown velocity, a controller is designed to maintain the robots following the leader at a certain distance behind, by using visual information about the position of the leader robot. The control system is proved to be asymptotically stable at the equilibrium point, which corresponds to the accomplishment of the navigation objective. Experimental results with two robots, a leader and a follower, are included to show the performance of the vision-based control system.

matcont is a matlab continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit cycles. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits in matcont . The implementation is done using the continuation of invariant subspaces, with the Riccati equations included in the defining system. A key feature is the possibility to initiate both types of homoclinic orbits interactively, starting from an equilibrium point and using a homotopy method. All known codimension-two homoclinic bifurcations are tested for during continuation. The test functions for inclination-flip bifurcations are implemented in a new and more efficient way. Heteroclinic orbits can now also be continued and an analogous homotopy method can be used for the initializa...

Using ideas from complexity theory and its application in the areas of ecology, biology, chemistry and medicine this paper shows how the paradigm of complexity is able to offer the conceptual frame in which they can project, evaluate and coordinate processes specific to the living world. Because a lot of environmental models were elaborated in last years, in this article we present some nonlinear techniques which can be used in stability analyses. Mathematical modelling plays a central and increasingly important role in evolution and ecology. This classification aims to help ecologists, biologists and environmentalists navigate the diversity of methods and techniques in mathematical modeling and develop a standardized approach to the application of mathematics in environmental research. Mathematical models have become indispensable tools in contemporary ecology and environmental sciences. We proposed to investigate a model for childhood epidemics such as measles, chickenpox, and mum...

A theoretical model describing the coupling of neutronics, thermohydraulics and fluidization in a fluidized bed nuclear reactor is presented. The stability of the system is investigated by linearizing and perturbing the system around its equilibrium points and identifying the root loci of the sytem. It is found that within the operational range, the eigenvalues are located in the negative part of the phase plane, implying linear stability. Simulations of transient conditions are performed, viz. a hypothetical startup transient and a quasistatic transient related to noise resulting from stochastic movements of the fuel particles. These simulations show that although the total power of the reactor may reach high values, the fuel temperature is well below safety limits at all times.

Neoclassical economics, governed by the first principle of thermodynamics, based on Newtonian mechanics and centred on the rational individual, reifies the human actions and preferences in unites of measure for calculating marginal utility, determining the indifference curve and the ‘equilibrium point’. But it is exactly this wish of the neoclassic economists to formalize and abstract which will later prove to be the main deficiency of the mainstream orthodox theory. Instead, we are being proposed to adopt an organic view upon the economy and to orientate towards identifying the quality of human actions and not their quantitative coordinates. The optics is changed under the influence of the second principle of thermodynamics, which emphasizes the fact that the economic process is irreversible and eminently characterized by entropy. Within human activities massive amounts of materials are engaged. These materials dry the planet of resources and exhaust the reserves supply for the fut...