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The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R k . The hyperchaotic output signal vðtÞ is a linear combination, specifically the mean of the individual chaotic signals, vðtÞ ¼ ðv 1 þ v 2 Þ=2. The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k / 1=R k should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k. For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.

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A particular case of chaos-to-chaos intermittency identified as on-off intermittency has experimentally been observed in a yttrium iron garnet sphere at high power ferromagnetic resonance. The theoretically predicted power law scaling with the exponent -1 has been detected in the dependencies of the mean "laminar" phase length on both static magnetic field and pumping microwave power. In the distribution of the laminar lengths a -3/2 power law was observed close to the onset of intermittency. PACS numbers: 75.40.Gb, 05.45.+b, 76.50.+g It has been demonstrated that dynamical systems with a simple type of symmetry can have striking features, e.g. , they can have attractors with riddled basins of attraction [1] or exhibit a particular type of intermittent bursting [2,3], recently called on-off intermittency by Platt, Spiegel, and Tresser [4]. Both phenomena are closely related [5,6] and have been reported to occur in a wide class of dynamical as well as stochastic systems [7]. Up to now, however, only few experimental observations of on-off intermittency [8,9] and riddled basins of attraction [10]have been presented, although the required symmetry of the system is expected to be rather common. Moreover, all experiments reported so far deal with the specific situation of electronic circuits where system parameters and variables can easily be controlled and the experimental setup models the theoretical equations more or less precisely.The important question concerning the observability of on-off intermittency in physical systems, which are not completely controlled like electronic circuits, is still open.In this Letter we report on the first observation of on-off intermittency in a spin-wave experiment representing a generic situation where the equations describing the experimental setup are unknown.On-off intermittency differs essentially from the wellknown Pomeau-Manneville[11]and crisis induced chaosto-chaos [12] intermittencies, although having common features with both of them. In dynamical systems it is related with a local bifurcation called blowout bifurcation by Ott and Sommerer [5]. This bifurcation defines the loss of stability of the smooth invariant manifold in phase space which exists due to the symmetry and contains the chaotic attractor. The main statistical properties of on-off intermittency can be obtained from the analysis of the simple linear map r"+i = ax"r", describing the dynamics of the distance from the invariant manifold in the linear vicinity [7]. The driving variable x" is determined by the chaotic dynamics on the manifold or can be a high-amplitude random signal for stochastic systems. For constant or periodic driving of x this map describes Pomeau-Manneville type III intermittency. Therefore, on-off intermittency can be defined as Pomeau Manneville type III-intermittency with an irregularly driven bifurcation parameterThe. amplitude of the irregular driving represents a new bifurcation parameter. Since the mean laminar phase length is determined by the averaged dynamics, it is not surpris...