Corpus ID: 224818902

Stability of cycling behaviour near a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock

  title={Stability of cycling behaviour near a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock},
  author={Claire M. Postlethwaite and Alastair M. Rucklidge},
  journal={arXiv: Dynamical Systems},
The well-known game of Rock--Paper--Scissors can be used as a simple model of competition between three species. When modelled in continuous time using differential equations, the resulting system contains a heteroclinic cycle between the three equilibrium solutions representing the existence of only a single species. The game can be extended in a symmetric fashion by the addition of two further strategies (`Lizard' and `Spock'): now each strategy is dominant over two of the remaining four… Expand
Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock
We study a system of ordinary differential equations in R5 that is used as a model both in population dynamics and in game theory, and is known to exhibit a heteroclinic network formed by three typesExpand
Behaviour of trajectories near a two-cycle heteroclinic network
We study behaviour of trajectories near a type Z heteroclinic network which is a union of two cycles. Analytical and numerical studies indicate that attractiveness of this network can be associatedExpand


Asymptotic stability of robust heteroclinic networks
We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heteroclinic networksExpand
Stability and bifurcations of heteroclinic cycles of type Z
Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper, we study stability properties of a class ofExpand
Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system
A simple dynamical model exhibiting sequential dynamics is studied, which shows that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria have two dimensional unstable manifolds that contain orbits connecting each equilibrium points to the next two equilibrium points in the chain. Expand
A competition between heteroclinic cycles
Competition between co-existing heteroclinic cycles that have a common heteroclinic connection is considered. A simple model problem, consisting of a system of ordinary differential equations in R4Expand
Stationary bifurcation to limit cycles and heteroclinic cycles
The authors consider stationary bifurcations with Z4.Z24 symmetry. For an open set of cubic coefficients in the normal form, we prove the existence of a limit cycle with frequency approximately modExpand
Regular and irregular cycling near a heteroclinic network
Heteroclinic networks are invariant sets containing more than one heteroclinic cycle. Such networks can appear robustly in equivariant vector fields. Previous authors have demonstrated thatExpand
Almost Complete and Equable Heteroclinic Networks
The relation between the heteroclinic network as a flow-invariant set and directed graphs of possible connections between nodes is examined and it is shown there are almost complete and equable realizations that can be closed by adding a number of extra nodes and connections. Expand
BF de Oliveira
  • and D Bazeia. Pattern formations driven by cyclic interactions: a brief review of recent developments. arXiv preprint arXiv:2009.09861
  • 2020
Pattern formations driven by cyclic interactions: A brief review of recent developments
Different aspects of biodiversity are overview, with focus on how it can be maintained based on mathematical modeling of last years, and the potential links to evolutionary game models of social systems are discussed. Expand
Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in $${\mathbb R}^4$$R4
An exhaustive list of finite subgroups of O(4) admitting the so-called simple heteroclinic cycles is compiled, and a new class is identified which is called pseudo-simple heterocinic cycles, which have at least one equilibrium with an unstable manifold which has dimension 2 due to a symmetry. Expand