On the dynamics of a non-linear Duopoly game model

On Asymptotic Effects of Boundary Perturbations in Exponentially Shaped Josephson Junctions

“…Proof The initial disturbances can be evaluated by means of (18), (19) and (21) 1 . Besides, since (21) 2 , the behaviour of the source term is determined.…”

“…In particular, when F = F (x, t, u), some non linear phenomena involve equation (1) both in superconductivity and biology and Dirichlet conditions in superconductivity refer to the phase boundary specifications [6,7,8,17], while in excitable systems occur when the pulse propagation in heart cells is studied [18]. Besides, Dirichlet problem is also considered for stability analysis and asymptotic behavior of reaction-diffusion systems solutions, [19,20], or in hyperbolic diffusion [21].…”

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

“…In the present paper we have extended [18], introducing self-and cross-diffusion terms. The spatial diffusion plays an important role in the process of population evolution, not only in ecology but also in many other fields of applied mathematics such as biochemistry or economics and the effect of self-and cross-diffusion on the population dynamics has been widely investigated theoretically by many mathematicians ( [19][20][21][22][23][24] and references therein). Self-diffusion terms model the random movement of individuals in both prey and predator populations.…”

Neimark–Sacker bifurcation and the generate cases of Kopel oligopoly model with different adjustment speed

“…A revised Kopel oligopoly model with extrapolative foresight was constructed by Gao, Zhong and Mei [11], and Neimark-Sacker bifurcation analysis showed the complex dynamics and the transitions between different dynamical systems. See more research about Kopel oligopoly model in [3,5,10,30,31,35]. As presented above in the related research, dynamical system theory was introduced as an important tool to explore the dynamics in oligopoly theory.…”