Organization of the Dynamics in a Parameter Plane of a Tumor Growth Mathematical Model

We report results of a numerical investigation on a two-dimensional cross-section of the parameter-space of a set of three autonomous, eight-parameter, first-order ordinary differential equations, ...

[1]  Amanda C Mathias,et al.  Periodicity suppression in continuous-time dynamical systems by external forcing. , 2012, Chaos.

[2]  Stephen P. Banks,et al.  Chaos in a Three-Dimensional Cancer Model , 2010, Int. J. Bifurc. Chaos.

[3]  Marco Thiel,et al.  Abundance of stable periodic behavior in a Red Grouse population model with delay: a consequence of homoclinicity. , 2010, Chaos.

[4]  Paulo C. Rech,et al.  Hopfield neural network: The hyperbolic tangent and the piecewise-linear activation functions , 2012, Neural Networks.

[5]  Paulo C. Rech,et al.  DYNAMICS OF A PARTICULAR LORENZ TYPE SYSTEM , 2010 .

[6]  Eduardo L. Brugnago,et al.  Chaos Suppression in a Sine Square Map through Nonlinear Coupling , 2011 .

[7]  J. Gallas,et al.  Structure of the parameter space of the Hénon map. , 1993, Physical review letters.

[8]  J. Gallas,et al.  Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit. , 2008, Physical review letters.

[9]  P. Glendinning,et al.  Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Jason A. C. Gallas,et al.  The Structure of Infinite Periodic and Chaotic Hub Cascades in Phase Diagrams of Simple Autonomous Flows , 2010, Int. J. Bifurc. Chaos.

[11]  Paulo C. Rech,et al.  Spiral periodic structure inside chaotic region in parameter-space of a Chua circuit , 2012, Int. J. Circuit Theory Appl..

[12]  Andrey Shilnikov,et al.  Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Paulo C. Rech,et al.  Dynamics of an erbium-doped fiber dual-ring laser , 2012 .

[14]  Paulo C. Rech.  Nonlinear dynamics investigation in parameter planes of a periodically forced compound KdV-Burgers equation , 2013 .

[15]  Ruedi Stoop,et al.  Real-world existence and origins of the spiral organization of shrimp-shaped domains. , 2010, Physical review letters.

[16]  Roberto Barrio,et al.  Crisis curves in nonlinear business cycles , 2012 .

[17]  Paulo C. Rech,et al.  Dynamics of a neuron model in different two-dimensional parameter-spaces , 2011 .

[18]  Iberê L. Caldas,et al.  Periodic window arising in the parameter space of an impact oscillator , 2010 .

[19]  J. Gallas,et al.  Self-organized distribution of periodicity and chaos in an electrochemical oscillator. , 2011, Physical chemistry chemical physics : PCCP.

[20]  Cristian Bonatto,et al.  Self-similarities in the frequency-amplitude space of a loss-modulated CO2 laser. , 2005, Physical review letters.

[21]  Gabriela A. Casas,et al.  Dynamics of Asymmetric Couplings of Two HéNon Maps , 2010, Int. J. Bifurc. Chaos.

[22]  J. G. Freire,et al.  Stern-Brocot trees in the periodicity of mixed-mode oscillations. , 2011, Physical chemistry chemical physics : PCCP.

[23]  M S Baptista,et al.  Experimental observation of a complex periodic window. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Vassilios Kovanis,et al.  Labyrinth bifurcations in optically injected diode lasers , 2010 .

[25]  Paulo C. Rech.  Self-Similarities and Period-Adding in the Parameter-Space of a Nonlinear Resonant Coupling Process , 2010 .

[26]  Holokx A. Albuquerque,et al.  Complex periodic structures in bi-dimensional bifurcation diagrams of a RLC circuit model with a nonlinear NDC device , 2009 .

[27]  Jason A. C. Gallas,et al.  How similar is the performance of the cubic and the piecewise-linear circuits of Chua? , 2010 .

[28]  Paulo C. Rech,et al.  The organization of periodicity and hyperchaos in an asymmetric coupling of two chaotic Rössler oscillators , 2013 .

[29]  Yoshisuke Ueda,et al.  Chaotic phase similarities and recurrences in a damped-driven Duffing oscillator. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  J. G. Freire,et al.  Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems , 2011 .

[31]  Paulo C. Rech,et al.  Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit , 2008 .

[32]  Paulo C. Rech,et al.  Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity. , 2010, Chaos.

[33]  J. G. Freire,et al.  Non-Shilnikov cascades of spikes and hubs in a semiconductor laser with optoelectronic feedback. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  C. DaCamara,et al.  Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model. , 2008, Chaos.