The concept of gamification uses the human behavior of indulging in gaming activities and combines it with their work with the purpose of enhancing, employee engagement. Game mechanics and dynamics are able to positively influence human behavior because they are designed to drive the players...

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the playersʼ strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the...

In this paper we deal with a class of non-differentiable functionals defined on a real reflexive Banach space X and depending on a real parameter of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{E}_\lambda(u)=L(u)-(J_1\circ T)(u)-\lambda (J_2\circ S)(u)}$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${L:X \rightarrow \mathbb R}$$</EquationSource> </InlineEquation> is a sequentially...</equationsource></inlineequation></equationsource></inlineequation>

In this chapter, we first precise the concept of dynamical systems, and then we introduce the concept of chaos, which is characterized by a sensitive dependence on initial conditions. To quantify this, dynamical (Lyapunov exponents) and probabilistic (dimensions) measures are introduced.