TY - JOUR A1 - Baptista, Murilo da Silva A1 - Grebogi, Celso A1 - Koberle, Roland T1 - Dynamically multilayered visual system of the multifractal fly JF - Physical review letters Y1 - 2006 U6 - https://doi.org/10.1103/PhysRevLett.97.178102 SN - 0031-9007 VL - 97 IS - 17 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Medrano-T., R. O. A1 - Baptista, Murilo da Silva A1 - Caldas, Ibere Luiz T1 - Shilnikov homoclinic orbit bifurcations in the Chua’s circuit JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We analytically describe the complex scenario of homoclinic bifurcations in the Chua’s circuit. We obtain a general scaling law that gives the ratio between bifurcation parameters of different nearby homoclinic orbits. As an application of this theoretical approach, we estimate the number of higher order subsidiary homoclinic orbits that appear between two consecutive lower order subsidiary orbits. Our analytical finds might be valid for a large class of dynamical systems and are numerically confirmed in the parameter space of the Chua’s circuit. Shilnikov homoclinic orbits are trajectories that depart from a fixed saddle-focus point, with specific eigenvalues, and return to it after an infinite amount of time (that is also true to time reversal evolution). That results in an orbit that is unstable and has an infinite period. These two main characteristics contribute in the hardness for its observation in a dynamical system as well as in nature. However, its presence reveals fundamental characteristics of the system involved, as the existence of unstable periodic orbits embedded in a chaotic set. Once the unstable periodic orbits give invariants quantities of this set,1 the Shilnikov homoclinic orbits are also related to the characteristics of the chaotic set. Their connection with the fundamental dynamical properties is verified in a wide variety of systems. A series of numerical and experimental investigations reveal how Shilnikov homoclinic orbits, in the vicinity of a chaotic attractor, determine its dynamical and topological properties.4 Thus, the Shilnikov orbits are related to the returning time of the trajectory of a CO2 laser,5 also to the topology of a glow-discharge system.6 Moreover, some class of spiking neurons are modeled by chaos governed by such orbits,7,8 and their presence are connected to the intermittence present in rabbit arteries.9 These orbits are shown to be behind the mechanism of noise-induced phenomena,10 and they are also responsible for the dynamics of an electrochemical oscillator.11 In this work, we contribute to the understanding of how Shilnikov homoclinic orbits appear on the parameter space of systems as the ones above mentioned, by showing that these orbits are not only distributed following an universal rule but also exist for large parameter variations. We then confirm our previsions in the Chua’s circuit system Y1 - 2006 U6 - https://doi.org/10.1063/1.2401060 SN - 1054-1500 VL - 16 IS - 4 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Baptista, Murilo da Silva A1 - Zhou, Changsong A1 - Kurths, Jürgen T1 - Information transmission in phase synchronous chaotic arrays N2 - We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize Y1 - 2006 UR - http://iopscience.iop.org/0256-307X/ U6 - https://doi.org/10.1088/0256-307X/23/3/010 SN - 0256-307X ER - TY - JOUR A1 - Pereira, Tiago A1 - Baptista, Murilo da Silva A1 - Reyes, Marcelo Bussotti A1 - Caldas, Ibere Luiz A1 - Sartorelli, José Carlos A1 - Kurths, Jürgen T1 - Global bifurcation destroying the experimental torus T-2 N2 - We show experimentally the scenario of a two-frequency torus T-2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.017201 ER - TY - JOUR A1 - Baptista, Murilo da Silva A1 - Pereira, Tiago A1 - Kurths, Jürgen T1 - Upper bounds in phase synchronous weak coherent chaotic attractors N2 - An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/01672789 U6 - https://doi.org/10.1016/j.physd.2006.02.007 SN - 0167-2789 ER -